What is the answer to x^2+2x-9=sqrt(6+4x+2x^2) ?

The answer to x^2+2x-9=sqrt(6+4x+2x^2) is x=3,x=-5

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x^2+2x-9=sqrt(6+4x+2x^2)

x^{2} + 2 x - 9 = 6 + 4 x + 2 x^{2}

x = 3, x = - 5

Solution steps

x^{2} + 2 x - 9 = 6 + 4 x + 2 x^{2}

Square both sides:

x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 81 = 6 + 4 x + 2 x^{2}

x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 81 = 6 + 4 x + 2 x^{2}

Solve

x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 81 = 6 + 4 x + 2 x^{2} : x = 3, x = - 5, x = - 1 + 6, x = - 1 - 6

x = 3, x = - 5, x = - 1 + 6, x = - 1 - 6

Verify Solutions:

x = 3

True

, x = - 5

True

, x = - 1 + 6

False

, x = - 1 - 6

False

The solutions are

x = 3, x = - 5

2 x^{2} + 6 x + 1 = 5

2 x - x^{2} = 1

x^{2} + 5 x = 0

x + x + 24 = 12

x - 2 = x

What is the answer to x^2+2x-9=sqrt(6+4x+2x^2) ?
The answer to x^2+2x-9=sqrt(6+4x+2x^2) is x=3,x=-5
Solve for x: x^2+2x-9=sqrt(6+4x+2x^2)
The solution is x=3,x=-5