Question 1093033
Solve for x.
sqrt{x^2-x-2} = sqrt{x^2+x+7} -1

I tried it and i got -5 but the calculator and my teacher said that the answer is supposed to be -2.
<pre>{{{sqrt(x^2 - x - 2) = sqrt(x^2 + x + 7) - 1}}}
{{{(sqrt(x^2 - x - 2))^2 = (sqrt(x^2 + x + 7) - 1)^2}}} ------- Squaring each side
{{{x^2 - x - 2 = x^2 + x + 7 - 2sqrt(x^2 + x + 7) + 1}}}
{{{x^2 - x - 2 = x^2 + x + 8 - 2sqrt(x^2 + x + 7)}}}
{{{2sqrt(x^2 + x + 7) = x^2 + x + 8 - x^2 + x + 2}}}
{{{2sqrt(x^2 + x + 7) = 2x + 10}}}
{{{4(x^2 + x + 7) = 4x^2 + 40x + 100}}} ------ Squaring each side
{{{4(x^2 + x + 7) = 4(x^2 + 10x + 25)}}}
{{{x^2 + x + 7 = x^2 + 10x + 25}}}
{{{x^2 - x^2 + x - 10x = 25 - 7}}}
- 9x = 18
{{{highlight_green(matrix(1,5, x, "=", 18/(- 9), "=", - 2))}}}</pre>