How do you solve using the completing the square method x^2 − x = 30?

1 Answer
Jothi S.
Aug 6, 2016

x=-5,6

Explanation:

x^2-x=30

1) Check the constant term is on the right side if not bring it to the right side .
2) Check the coefficient of x^2 is 1 if not Make the coefficient of x^2 as 1

x^2-x=30

Add both side (coefficient of x/2)^2

Coefficient of x is -1 so add (-1/2)^2, both side

x^2-x+(1/2)^2=30 +(1/2)^2 use the identity (a-b)^2=a^2-2ab+b^2

x^2-x+(1/2)^2=(x-1/2)^2

(x-1/2)^2=30+1/4

(x-1/2)^2=121/4
squaring on both side

(x-1/2)=+-sqrt(121/4)

(x-1/2)=+-11/2

x=1/2+11/2, x=1/2-11/2
x=12/2 or x=-10/2

x=-5,6

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