What is the answer to x^2-x+2sqrt(x^2-x-5)=8 ?

The answer to x^2-x+2sqrt(x^2-x-5)=8 is x=-2,x=3

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x^2-x+2sqrt(x^2-x-5)=8

x^{2} - x + 2 x^{2} - x - 5 = 8

x = - 2, x = 3

Solution steps

x^{2} - x + 2 x^{2} - x - 5 = 8

Remove square roots

4 x^{2} - 4 x - 20 = x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 64

Solve

4 x^{2} - 4 x - 20 = x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 64 : x = - 2, x = 3, x = \frac{1 + 57}{2}, x = \frac{1 - 57}{2}

x = - 2, x = 3, x = \frac{1 + 57}{2}, x = \frac{1 - 57}{2}

Verify Solutions:

x = - 2

True

, x = 3

True

, x = \frac{1 + 57}{2}

False

, x = \frac{1 - 57}{2}

False

The solutions are

x = - 2, x = 3

1 - 8 x = 5 + 3 x + 9

9 x - 9 - 3 = 0

0 = 3 - \frac{3 x - 1}{2}

What is the answer to x^2-x+2sqrt(x^2-x-5)=8 ?
The answer to x^2-x+2sqrt(x^2-x-5)=8 is x=-2,x=3
Solve for x: x^2-x+2sqrt(x^2-x-5)=8
The solution is x=-2,x=3