What is the answer to x^2-6x=13sqrt(x^2-6x)-36 ?

The answer to x^2-6x=13sqrt(x^2-6x)-36 is x=-2,x=8,x=3(1+sqrt(10)),x=3(1-sqrt(10))

Solve for x: x^2-6x=13sqrt(x^2-6x)-36

The solution is x=-2,x=8,x=3(1+sqrt(10)),x=3(1-sqrt(10))

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x^{2} - 6 x = 13 x^{2} - 6 x - 36

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

Decimal Notation

x = - 2, x = 8, x = 12.48683 \dots, x = - 6.48683 \dots

Solution steps

x^{2} - 6 x = 13 x^{2} - 6 x - 36

Remove square roots

x^{4} - 12 x^{3} + 108 x^{2} - 432 x + 1296 = 169 x^{2} - 1014 x

Solve

x^{4} - 12 x^{3} + 108 x^{2} - 432 x + 1296 = 169 x^{2} - 1014 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)

True

, x = 3 (1 - 10)

True

The solutions are

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

y = 3 + y^{2} - 5

x^{2} = 4

x + 5 + x = 5

2 1 - x = 16 - 3 x - 1

2 x - 1 = 0

What is the answer to x^2-6x=13sqrt(x^2-6x)-36 ?
The answer to x^2-6x=13sqrt(x^2-6x)-36 is x=-2,x=8,x=3(1+sqrt(10)),x=3(1-sqrt(10))
Solve for x: x^2-6x=13sqrt(x^2-6x)-36
The solution is x=-2,x=8,x=3(1+sqrt(10)),x=3(1-sqrt(10))