What is the answer to x^2+15x+sqrt(x^2+15x)=20 ?

The answer to x^2+15x+sqrt(x^2+15x)=20 is x=1,x=-16

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x^2+15x+sqrt(x^2+15x)=20

x^{2} + 15 x + x^{2} + 15 x = 20

x = 1, x = - 16

Solution steps

x^{2} + 15 x + x^{2} + 15 x = 20

Remove square roots

x^{2} + 15 x = x^{4} + 30 x^{3} + 185 x^{2} - 600 x + 400

Solve

x^{2} + 15 x = x^{4} + 30 x^{3} + 185 x^{2} - 600 x + 400 : x = 1, x = - 16, x = \frac{- 15 + 5 13}{2}, x = \frac{- 15 - 5 13}{2}

x = 1, x = - 16, x = \frac{- 15 + 5 13}{2}, x = \frac{- 15 - 5 13}{2}

Verify Solutions:

x = 1

True

, x = - 16

True

, x = \frac{- 15 + 5 13}{2}

False

, x = \frac{- 15 - 5 13}{2}

False

The solutions are

x = 1, x = - 16

4 x 3 - x = 0

2 x + 20 = 15 + 3 x

x - 5 = x + 1

x - 5 = x + 7

What is the answer to x^2+15x+sqrt(x^2+15x)=20 ?
The answer to x^2+15x+sqrt(x^2+15x)=20 is x=1,x=-16
Solve for x: x^2+15x+sqrt(x^2+15x)=20
The solution is x=1,x=-16