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

1 Answer
Aug 6, 2016

Answer:

#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#