SOLUTION: 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.

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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.
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
sqrt(x^2 - x - 2) = sqrt(x^2 + x + 7) - 1
x^2 - x - 2 = (sqrt(x^2 + x + 7) - 1)^2
Let's simplify the equation on the right:
(sqrt(x^2 + x + 7) - 1)^2 = 8 + x + x^2 - 2 sqrt(x^2 + x + 7):
x^2 - x - 2 = 8 + x + x^2 - 2 sqrt(x^2 + x + 7)
2 sqrt(x^2 + x + 7) = 2 x + 10
4 (x^2 + x + 7) = (2 x + 10)^2
4 x^2 + 4 x + 28 = (2 x + 10)^2
4 x^2 + 4 x + 28 = 4 x^2 + 40 x + 100
-36 x - 72 = 0
-36 (x + 2) = 0
x + 2 = 0
x = -2
:
I hope this helps, it was a lot of writing.
John

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
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.

------- Squaring each side ------ Squaring each side - 9x = 18