What is the answer to x^2-6x=36-5sqrt(x^2-6x) ?

The answer to x^2-6x=36-5sqrt(x^2-6x) is x=-2,x=8

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x^2-6x=36-5sqrt(x^2-6x)

x^{2} - 6 x = 36 - 5 x^{2} - 6 x

x = - 2, x = 8

Solution steps

x^{2} - 6 x = 36 - 5 x^{2} - 6 x

Remove square roots

x^{4} - 12 x^{3} - 36 x^{2} + 432 x + 1296 = 25 x^{2} - 150 x

Solve

x^{4} - 12 x^{3} - 36 x^{2} + 432 x + 1296 = 25 x^{2} - 150 x : x = - 2, x = 8, x = 3 (1 + 10), x = 3 (1 - 10)

x = - 2, x = 8, x = 3 (1 + 10), x = 3 (1 - 10)

Verify Solutions:

x = - 2

True

, x = 8

True

, x = 3 (1 + 10)

False

, x = 3 (1 - 10)

False

The solutions are

x = - 2, x = 8

4 x + 8 = 6

x - 6 + 3 = 10

2 x = 8

2 x + 3 - x + 5 = - 1

x + 7 x + 2 = 0

What is the answer to x^2-6x=36-5sqrt(x^2-6x) ?
The answer to x^2-6x=36-5sqrt(x^2-6x) is x=-2,x=8
Solve for x: x^2-6x=36-5sqrt(x^2-6x)
The solution is x=-2,x=8