What is the answer to x^2+5x-19=sqrt(x^2+5x+1) ?

The answer to x^2+5x-19=sqrt(x^2+5x+1) is x=3,x=-8

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x^2+5x-19=sqrt(x^2+5x+1)

x^{2} + 5 x - 19 = x^{2} + 5 x + 1

x = 3, x = - 8

Solution steps

x^{2} + 5 x - 19 = x^{2} + 5 x + 1

Square both sides:

x^{4} + 10 x^{3} - 13 x^{2} - 190 x + 361 = x^{2} + 5 x + 1

x^{4} + 10 x^{3} - 13 x^{2} - 190 x + 361 = x^{2} + 5 x + 1

Solve

x^{4} + 10 x^{3} - 13 x^{2} - 190 x + 361 = x^{2} + 5 x + 1 : x = 3, x = - 8, x = \frac{- 5 + 85}{2}, x = \frac{- 5 - 85}{2}

x = 3, x = - 8, x = \frac{- 5 + 85}{2}, x = \frac{- 5 - 85}{2}

Verify Solutions:

x = 3

True

, x = - 8

True

, x = \frac{- 5 + 85}{2}

False

, x = \frac{- 5 - 85}{2}

False

The solutions are

x = 3, x = - 8

x^{2} = 2017

(2 x - 3)^{\frac{1}{3}} = - 1

8 - x = 0

x - 9 + x + 6 = 5

3 \cdot X - 6 = - 3

What is the answer to x^2+5x-19=sqrt(x^2+5x+1) ?
The answer to x^2+5x-19=sqrt(x^2+5x+1) is x=3,x=-8
Solve for x: x^2+5x-19=sqrt(x^2+5x+1)
The solution is x=3,x=-8