配方法解方程,x的平方+10x=9=0

题目

配方法解方程,x的平方+10x=9=0

答案

x" + 10x + 9 = 0
x" + 10x + 25 - 16 = 0
( x + 5 )" - 4" = 0
( x + 5 - 4 )( x + 5 + 4 ) = 0
( x + 1 )( x + 9 ) = 0
解方程得
x1 = -1
x2 = -9
如果 x" + 10x = 9,也就是
x" + 10x - 9 = 0
同样 x" + 10x + 25 - 34 = 0
( x + 5 )" - ( √34 )" = 0
( x + 5 + √34 )( x + 5 - √34 ) = 0
解方程得
x1 = -5 - √34
x2 = -5 + √34