SOLUTION: √(x^2-x+7)=2(x^2-x)-1

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Question 863488: √(x^2-x+7)=2(x^2-x)-1
Answer by mananth(16946) About Me  (Show Source):
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sqrt%28x%5E2-x%2B7%29=2%28x%5E2-x%29-1

let x%5E2-x=a
sqrt%28a%2B7%29=2a-1

square both sides
a%2B7=+%282a-1%29%5E2
a%2B7=+4a%5E2-4a%2B1
Rearrange
4a%5E2-5a-6=0
factorize

4a%5E2-8a%2B3a-6=0

4a(a-2)+3(a-2)=0
(4a+3)(a-2)=0

either 4a+3=0 OR a-2 =0
substitute a
4%28x%5E2-x%29%2B3=0
4x%5E2-4x%2B3=0
4x%5E2-4x=-3
add 1 both side
4x%5E2-4x%2B1=-3%2B1
%282x-1%29%5E2=-2
square root
(2x-1) = +/-sqrt%28-2%29

2x = 1+/- sqrt%28-2%29
x= (1+/- sqrt(-2))/2
Now
a-2=0
x^2-x-2=0
x^2-2x+x-2=0
x(x-2)+1(x-2)=0
(x-2)(x+1)=0
x=2 OR -1