初二数学实数计算题 初二数学实数计算题
\u6570\u5b66\u521d\u4e8c\u5b9e\u6570\u8ba1\u7b97\u9898\u53ca\u7b54\u6848\uff08\u4e00\u767e\u9053\uff09(1)99²\uff0d2.99² (2)80\u00d73.5²\uff0b160\u00d73.5\u00d71.5\uff0b80\u00d71.5² (3)181²\uff0d61²\u00f7301²\uff0d181²
(4)5x\uff0d5y\uff0b5z (5)-5a²+25a-5a (6)2a(b+c)-3(b+c) (7)(ab+a)+(b+1)
(8)-4m³+16m³-28m (9)16x-25x³y² (10)36m²a-9m²a²-36m²
\u221a32-3\u221a1/2+\u221a2
\u221a12+\u221a27/\u221a3-\u221a1/3\u00d7\u221a12
\u221a50+\u221a30/\u221a8-4
\uff08\u221a6-2\u221a15\uff09\u00d7\u221a3-6\u221a1/2
\u221a2/3-4\u221a216+43\u221a1/6
\u221a8+\u221a30-\u221a2
\u221a40-5\u221a1/10+\u221a10
\u221a2+\u221a8/\u221a2
\u221a2/9+\u221a50+\u221a32
\uff081-\u221a3\uff09\uff08\u221a3+2\uff09
\uff08\u221a8+3\u221a6\uff09\u00f7\u221a2-\u221a3\u00d7\u221a0.7
\uff08-3+\u221a6\uff09\uff08-3-\u221a6\uff09-\uff08\u221a3-1/\u221a3\uff09²
³\u221a0.125-\u221a3 1/16+³\u221a\uff081-7/8\uff09²
\u221a2/3-\u221a216+42\u221a1/6
\u89e3\u65b9\u7a0b\u221a3 X-1=\u221a2 X
\u6c42X
{\u221a5 X-3\u221a Y=1}
{\u221a3 X-\u221a5 Y=2}
\u6ce8\uff1aX\u5168\u90e8\u4e0d\u5728\u6839\u53f7\u5185
\u221a\uff081/2x\uff09^2\uff0b10/9x^2
=\u221a[1/(4x^2)+10/(9x^2)]
=\u221a49/36x^2
\u82e5x>0,=7/(6x)
\u82e5x<0,=-7/(6x)
\u221aa^4mb^2n\uff0b1
=\u221a(a^2mb^n)^2\uff0b1
=a^2mb^n\uff0b1
\u221a\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09
=\u221a[4a^4(a+2)][(a+2)(a+1)]
=\u221a[4a^4(a+2)^2(a+1)]
=2a^2(a+2)\u221a(a+1)
. 3\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09
\u7b54\u68483\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09
= 3\u00d7\u221a6/6-4\u00d75\u221a2+30\u00d7\u221a6/3
\uff1d\u221a6/2-20\u221a2+10\u221a6
2. \uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2
\u9898\u662f\u8fd9\u6837\u7684\u4e8c\u5206\u4e4b\u4e00\u51cf\u6839\u53f72\u4e58\u4ee5\u4e8c\u5206\u4e4b\u4e00\u52a0\u6839\u53f72
\u7b54\u6848\uff1a\uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2
=\uff081-\u221a2\uff09*\uff081-\u221a2\uff09\uff0f4
\uff1d\uff081\uff0d2\uff09\uff0f4
\uff1d\uff0d1\uff0f4
1.3\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09 \u7b54\u68483\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09 = 3\u00d7\u221a6/6-4\u00d75\u221a2+30\u00d7\u221a6/3 \uff1d\u221a6/2-20\u221a2+10\u221a6 2. \uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2 \u9898\u662f\u8fd9\u6837\u7684\u4e8c\u5206\u4e4b\u4e00\u51cf\u6839\u53f72\u4e58\u4ee5\u4e8c\u5206\u4e4b\u4e00\u52a0\u6839\u53f72 \u7b54\u6848\uff1a\uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2 =\uff081-\u221a2\uff09*\uff081-\u221a2\uff09\uff0f4 \uff1d\uff081\uff0d2\uff09\uff0f4 \uff1d\uff0d1\uff0f4 3.\u221a\uff081/2x\uff09^2\uff0b10/9x^2 \u221a[\uff081/2x\uff09^2\uff0b10/9x^2] =\u221a(x^2/4+10x^2/9) =\u221a(9x^2/36+40x^2/36) =\u221a(49x^2/36) =7x/6; 4.\u221aa^4mb^2n\uff0b1\uff08a\u3001b\u4e3a\u6b63\u6570\uff09 [\u221a(a^4mb^2n)]\uff0b1\uff08a\u3001b\u4e3a\u6b63\u6570\uff09 =a^2mb^n+1; 5.\u221a\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09\uff08a>=0\uff09 \u221a[\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09]\uff08a>=0\uff09 =\u221a[4a^4(a+2)(a+2)(a+1)] =\u221a[(2a^2)^2(a+2)^2(a+1)] =2a^2(a+2)\u221a(a+1). \u592a\u591a\u4e86\u5440\uff0c\u53ea\u80fd\u8fd9\u6837\u4e86\uff0c\u6211\u8fd8\u6709\u4e8b \u60a8\u597d\uff01 \u24605\u221a8-2\u221a32+\u221a50 =5*3\u221a2-2*4\u221a2+5\u221a2 =\u221a2(15-8+5) =12\u221a2 \u2461\u221a6-\u221a3/2-\u221a2/3 =\u221a6-\u221a6/2-\u221a6/3 =\u221a6/6 \u2462(\u221a45+\u221a27)-(\u221a4/3+\u221a125) =(3\u221a5+3\u221a3)-(2\u221a3/3+5\u221a5) =-2\u221a5+7\u221a5/3 \u2463(\u221a4a-\u221a50b)-2(\u221ab/2+\u221a9a) =(2\u221aa-5\u221a2b)-2(\u221a2b/2+3\u221aa) =-4\u221aa-6\u221a2b \u2464\u221a4x*(\u221a3x/2-\u221ax/6) =2\u221ax(\u221a6x/2-\u221a6x/6) =2\u221ax*(\u221a6x/3) =2/3*x*\u221a6 \u2465(x\u221ay-y\u221ax)\u00f7\u221axy =x\u221ay\u00f7\u221axy-y\u221ax\u00f7\u221axy =\u221ax-\u221ay \u2466(3\u221a7+2\u221a3)(2\u221a3-3\u221a7) =(2\u221a3)^2-(3\u221a7)^2 =12-63 =-51 \u2467(\u221a32-3\u221a3)(4\u221a2+\u221a27) =(4\u221a2-3\u221a3)(4\u221a2+3\u221a3) =(4\u221a2)^2-(3\u221a3)^2 =32-27 =5 \u2468(3\u221a6-\u221a4)² =(3\u221a6)^2-2*3\u221a6*\u221a4+(\u221a4)^2 =54-12\u221a6+4 =58-12\u221a6 \u2469\uff081+\u221a2-\u221a3\uff09\uff081-\u221a2+\u221a3\uff09 =[1+(\u221a2-\u221a3)][1-(\u221a2-\u221a3)] =1-(\u221a2-\u221a3)^2 =1-(2+3+2\u221a6) =-4-2\u221a6 1. =5\u221a5 - 1/25\u221a5 - 4/5\u221a5 =\u221a5*(5-1/25-4/5) =24/5\u221a5 2.=\u221a144+576 =\u221a720 =12\u221a5 3.)\u221a(8/13)^2-(2/13)^2 = \u221a(8/13+2/13)(8/13-2/13) =(2/13)\u221a15
\u89e3\u65b9\u7a0b\u221a3 X-1=\u221a2 X
\u6c42X
{\u221a5 X-3\u221a Y=1}
{\u221a3 X-\u221a5 Y=2}
\u6ce8\uff1aX\u5168\u90e8\u4e0d\u5728\u6839\u53f7\u5185
\u221a\uff081/2x\uff09^2\uff0b10/9x^2
=\u221a[1/(4x^2)+10/(9x^2)]
=\u221a49/36x^2
\u82e5x>0,=7/(6x)
\u82e5x<0,=-7/(6x)
\u221aa^4mb^2n\uff0b1
=\u221a(a^2mb^n)^2\uff0b1
=a^2mb^n\uff0b1
\u221a\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09
=\u221a[4a^4(a+2)][(a+2)(a+1)]
=\u221a[4a^4(a+2)^2(a+1)]
=2a^2(a+2)\u221a(a+1)
. 3\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09
\u7b54\u68483\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09
= 3\u00d7\u221a6/6-4\u00d75\u221a2+30\u00d7\u221a6/3
\uff1d\u221a6/2-20\u221a2+10\u221a6
2. \uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2
\u9898\u662f\u8fd9\u6837\u7684\u4e8c\u5206\u4e4b\u4e00\u51cf\u6839\u53f72\u4e58\u4ee5\u4e8c\u5206\u4e4b\u4e00\u52a0\u6839\u53f72
\u7b54\u6848\uff1a\uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2
=\uff081-\u221a2\uff09*\uff081-\u221a2\uff09\uff0f4
\uff1d\uff081\uff0d2\uff09\uff0f4
\uff1d\uff0d1\uff0f4
1.3\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09 \u7b54\u68483\u221a\uff081/6\uff09-4\u221a\uff0850\uff09+30\u221a\uff082/3\uff09 = 3\u00d7\u221a6/6-4\u00d75\u221a2+30\u00d7\u221a6/3 \uff1d\u221a6/2-20\u221a2+10\u221a6 2. \uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2 \u9898\u662f\u8fd9\u6837\u7684\u4e8c\u5206\u4e4b\u4e00\u51cf\u6839\u53f72\u4e58\u4ee5\u4e8c\u5206\u4e4b\u4e00\u52a0\u6839\u53f72 \u7b54\u6848\uff1a\uff081-\u6839\u53f72\uff09/2\u4e58\u4ee5\uff081\uff0b\u6839\u53f72\uff09\uff0f2 =\uff081-\u221a2\uff09*\uff081-\u221a2\uff09\uff0f4 \uff1d\uff081\uff0d2\uff09\uff0f4 \uff1d\uff0d1\uff0f4 3.\u221a\uff081/2x\uff09^2\uff0b10/9x^2 \u221a[\uff081/2x\uff09^2\uff0b10/9x^2] =\u221a(x^2/4+10x^2/9) =\u221a(9x^2/36+40x^2/36) =\u221a(49x^2/36) =7x/6; 4.\u221aa^4mb^2n\uff0b1\uff08a\u3001b\u4e3a\u6b63\u6570\uff09 [\u221a(a^4mb^2n)]\uff0b1\uff08a\u3001b\u4e3a\u6b63\u6570\uff09 =a^2mb^n+1; 5.\u221a\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09\uff08a>=0\uff09 \u221a[\uff084a^5\uff0b8a^4\uff09\uff08a^2\uff0b3a\uff0b2\uff09]\uff08a>=0\uff09 =\u221a[4a^4(a+2)(a+2)(a+1)] =\u221a[(2a^2)^2(a+2)^2(a+1)] =2a^2(a+2)\u221a(a+1). \u592a\u591a\u4e86\u5440\uff0c\u53ea\u80fd\u8fd9\u6837\u4e86\uff0c\u6211\u8fd8\u6709\u4e8b \u60a8\u597d\uff01 \u24605\u221a8-2\u221a32+\u221a50 =5*3\u221a2-2*4\u221a2+5\u221a2 =\u221a2(15-8+5) =12\u221a2 \u2461\u221a6-\u221a3/2-\u221a2/3 =\u221a6-\u221a6/2-\u221a6/3 =\u221a6/6 \u2462(\u221a45+\u221a27)-(\u221a4/3+\u221a125) =(3\u221a5+3\u221a3)-(2\u221a3/3+5\u221a5) =-2\u221a5+7\u221a5/3 \u2463(\u221a4a-\u221a50b)-2(\u221ab/2+\u221a9a) =(2\u221aa-5\u221a2b)-2(\u221a2b/2+3\u221aa) =-4\u221aa-6\u221a2b \u2464\u221a4x*(\u221a3x/2-\u221ax/6) =2\u221ax(\u221a6x/2-\u221a6x/6) =2\u221ax*(\u221a6x/3) =2/3*x*\u221a6 \u2465(x\u221ay-y\u221ax)\u00f7\u221axy =x\u221ay\u00f7\u221axy-y\u221ax\u00f7\u221axy =\u221ax-\u221ay \u2466(3\u221a7+2\u221a3)(2\u221a3-3\u221a7) =(2\u221a3)^2-(3\u221a7)^2 =12-63 =-51 \u2467(\u221a32-3\u221a3)(4\u221a2+\u221a27) =(4\u221a2-3\u221a3)(4\u221a2+3\u221a3) =(4\u221a2)^2-(3\u221a3)^2 =32-27 =5 \u2468(3\u221a6-\u221a4)² =(3\u221a6)^2-2*3\u221a6*\u221a4+(\u221a4)^2 =54-12\u221a6+4 =58-12\u221a6 \u2469\uff081+\u221a2-\u221a3\uff09\uff081-\u221a2+\u221a3\uff09 =[1+(\u221a2-\u221a3)][1-(\u221a2-\u221a3)] =1-(\u221a2-\u221a3)^2 =1-(2+3+2\u221a6) =-4-2\u221a6 1. =5\u221a5 - 1/25\u221a5 - 4/5\u221a5 =\u221a5*(5-1/25-4/5) =24/5\u221a5 2.=\u221a144+576 =\u221a720 =12\u221a5 3.)\u221a(8/13)^2-(2/13)^2 = \u221a(8/13+2/13)(8/13-2/13) =(2/13)\u221a15 \u53c2\u8003\u8d44\u6599\uff1a
2.已知方程x^2-5x+3=0的两个根为x1,x2，计算下列各式的值（不解方程）
(1)x1+x2;
(2)x1*x2;
(3)1/x1+1/x2;
(4)x1^2+x2^2.
随堂作业—基础达标
1.如果方程ax^2+bx+c=0(a=/0)的两根是x1，x2，那么x1+x2=________,x1*x2=________.
2.已知x1，x2是方程2x^2+3x-4=0的两个根，那么x1+x2=________;x1*x2=_______;1/x1+1/x2=________;x1^2+x2^2=________;(x1+1)(x2+1)=___________.
3.已知一元二次方程2x^2-3x-1=0的两根为x1，x2，则x1+x2=________.
4.若方程x^2+x-1=0的两根分别为x1，x2，则x1^2+x2^2=________.
5.已知x1，x2是关于x的方程x^2+mx+m=0的两个实数根，且x1+x2=1/3，则x1*x2=___________.
6.以3，-1为根，且二次项系数为3的一元二次方程式（ ）
A.3x^2-2x+3=0
B.3x^2+2x-3=0
C.3x^2-6x-9=0
D.3x^2+6x-9=0
7.设x1，x2是方程2x^2-2x-1=0的两个根，利用根与系数的关系，求下列各式的值：
(1) (2x1+1)(2x2+1);
(2) (x1^2+2)(x2^2+2);
(3) x1-x2.
课后作业—基础拓展
1.（巧解题）已知 α^2+α-1=0，β^2+β-1=0，且α不等于β，则αβ+α+β的值为（ ）
A.2
B.-2
C.-1
D.0
2.（易错题）已知三角形两边长分别为2和9，第三边的长为一元二次方程式x^2-14x+48=0的一个根，则这个三角形的周长为（ ）
A.11
B.17
C.17或19
D.19
3.若关于x的一元二次方程x^2+kx+4k^2-3=0的两个实数根分别是x1，x2，且满足x1+x2=x1*x2,则k的值为（ ）
A.-1或3/4
B.-1
C.3/4
D.不存在
4.（一题多解）已知方程2x^2+mx-4=0的一根为-2，求它的另一条根的值.（用两种方法求解）
答案：1.-P Q
2. 5 3 第三个式子合并(X1+X2)/X1*X2=5/3 第四个式子=(X1+X2)^2-2X1*X2 =19
随堂作业—基础达标
1.-B/A C/A
2.-3/2 -2 3/4 25/4
3. 3/2
4. 3
5. -1/3
6. C
7.设x1，x2是方程2x^2-2x-1=0的两个根，利用根与系数的关系，求下列各式的值：
(1) (2x1+1)(2x2+1); 展开=2
因为X1+X2=1 X1X2=-1/2
(2) (x1^2+2)(x2^2+2); 展开=29/4
(3) x1-x2.=(X1-X2)^2开平方=X1^2+X2^2-2X1X2=
=(X1+X2)^2-4X1X2 =3开平方
课后作业—基础拓展
1.（巧解题）已知 α^2+α-1=0，β^2+β-1=0，且α不等于β，则αβ+α+β的值为（B ）
A.2
B.-2
C.-1
D.0
2.（易错题）已知三角形两边长分别为2和9，第三边的长为一元二次方程式x^2-14x+48=0的一个根，则这个三角形的周长为（ D）注意两边之和大于第三边 之差小于第三边 所以只能是8
A.11
B.17
C.17或19
D.19
3.若关于x的一元二次方程x^2+kx+4k^2-3=0的两个实数根分别是x1，x2，且满足x1+x2=x1*x2,则k的值为（c ） 注意：当k为-1时候 原方程的b^2-4ac小于0
A.-1或3/4
B.-1
C.3/4
D.不存在
4.（一题多解）已知方程2x^2+mx-4=0的一根为-2，求它的另一条根的值.（用两种方法求解）
1.两根之和=-M/2=-2+X2 两根之积=-2
所以X2=1 M=2
2.（-b+或者-根号下b^2-4ac）/2a=-2
解下列方程
1. (2x-1)^2-1=0
1
2. —（x+3)^2=2
2
3. x^2+2x-8=0
4. 3x^2=4x-1
5. x(3x-2)-6x^2=0
6. (2x-3)^2=x^2
一.配完全平方式（直接写答案）
1. x^2-4x+___________=（x-___________）^2
2. x^2+mx+9是一个完全平方式，则m=_____
二.配方法解一元二次方程（需要过程）
3.用配方程解一元二次方程
x^2-8x-9=0
基础达标
1用配方法解方程x^2-6x-5=0,配方得（ ）
A.（x-6)^2=14
B.(x-3)^=8
C.(x-3)^=14
D.(x-6)^2=41
2.将二次三项式2x^-3x+5配方，正确的是（ ）
3 31
A.（x- —)^2+ —
4 16
3 34
B.（x- —)^2- —
4 16
3 31
C.2(x- —）^2+ —
4 16
3 31
D.2（x- —)^2+ —
4 8
3.填空：
1. x^2+8x+______=（x+______)^2
2.2x^2-12x+______=2（x-______）^2
4.用配方法解下列方程（要过程）
1. x^+5x+3=0
2. 2x^2-x-3=0
基础扩展
1.已知(x^2+y^2)(x^2+y^2+2)-8=0,则x^2+y^2的值是（ ）
A.-4
B. 2
C.-1或4
D.2或4
2.（综合体）用配方法解关於x^2+2mx-n^2=0（要求写出过程）
3.（创新题）小丽和小晴是一对好朋友，但小丽近期沉迷与网络，不求上进，小晴决定不交这个朋友，就给了她一个一元二次方程说：“解这个方程吧，这就是我们的结果！”小丽解完这个方程大吃一惊，原来把这两个跟放在一起是“886”（网络语“拜拜了”）。同学你能设计一个这样的一元二次方程麼？
4.（开放探究题）设代数式2x^2+4x-3=M，用配方法说明：无论x取何值，M总不小於一定值，并求出该值（要求全过程）
答案：【解下列方程】
1、(2X)^2-1=0
移项，得：(2X)^2=1
开平方，得：2X=+-1
方程两边都除以2，得：X=+-1/2
2、1/2(X+3)^2=2
方程两边都乘以2，得：(X+3)^2=4
开平方，得：X+3=+-2
方程两边都减去3，得：X=-1或-5
3、X^2+2X-8=0
左边进行因式分解，得：(X+2)(X-4)=0
X+2=0或X-4=0
X=-2或X=4
4、3X^2=4X-1
移项，得：3X^2-4X+1=0
左边进行因式分解，得：(3X-1)(X-1)=0
3X-1=0或X-1=0
X=1/3或X=1
5、X(3X-2)-6X^2=0
3X^2-2X-6X^2=0
整理，得：-3X^2-2X=0
方程两边都除以-1，得：3X^2+2X=0
左边进行因式分解，得：X(3X+2)=0
X=0或3X+2=0
X=0或X=-2/3
6、(2X-3)^2=X^2
4X^2-12X+9=X^2
方程两边都减去X^2，得：3X^2-12X+9=0
方程两边都除以3，得：X^2-4X+3=0
左边进行因式分解，得：(X-1)(X-3)=0
X-1=0或X-3=0
X=1或X=3
【一、配完全平方式】
1、 x^2-4x+4=（x-2）^2
2、 x^2+mx+9是一个完全平方式，则m=6
【二、配方法解一元二次方程】
X^2-8X-9=0
X^2-8X=9
X^2-8X+16=9+16
(X-4)^2=25
(X-4)^2=5^2
X-4=+-5
X=9或-1
【基础达标】
1、C
2、D
3、填空
① x^2+8x+16=（x+4)^2
②2x^2-12x+18=2（x-3）^2
4.用配方法解下列方程（要过程）
①X^+5X+3=0
X^+5X=-3
x^+5X+(5/2)^2=(5/2)^2-3
(X+5/2)^2=13/4
X+5/2=+-√13/2
X=(√13-5)/2或-(√13+5)/2
②2X^2-X-3=0
X^2-1/2X=3/2
X^2-1/2X+(1/4)^2=3/2+(1/4)^2
(X-1/4)^2=25/16
X-1/4=+-5/4
X=3/2或X=-1
【基础扩展】
1、B
2、X^2+2mX-n^2=0
X^2+2mX=n^2
X^2+2mX+m^2=n^2+m^2
(X+m)^2=n^2+m^2
X+m=+-√(n^2+m^2)
X=-m+-√(n^2+m^2)
3、不是很清楚题意，两个根放在一起是886三个数，是加起来还是怎么组合呢，如果是8和6的话，很简单，(X-8)(X-6)=0就可以了，展开就是X^2-14X+48=0
如果两个根是88和6，(X-88)(X-6)=0，展开就是X^2-94X+528=0
4、2X^2+4X-3=M
M=2X^2+4X-3
=2(X^2+2X)-3
=2(X^2+2X+1-1)-3
=2(X^2+2X+1)-5
=2(X+1)^2-5
无论X取何值，2(X+1)^2恒大于0，则M恒大于-5。
【配方法具体过程如下】
1、将此一元二次方程化为ax^2+bx+c=0的形式(此一元二次方程满足有实根)
2、将二次项系数化为1
3、将常数项移到等号右侧
4、等号左右两边同时加上一次项系数一半的平方
5、将等号左边的代数式写成完全平方形式
6、左右同时开平方
7、整理即可得到原方程的根
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