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(sqrt(10)-1),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(sqrt(10)-1),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 (10 - 1), x = - 3 (1 + 10)

Decimal Notation

x = 2, x = - 8, x = 6.48683 \dots, x = - 12.48683 \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 (10 - 1), x = - 3 (1 + 10)

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

Verify Solutions:

x = 2

True

, x = - 8

True

, x = 3 (10 - 1)

True

, x = - 3 (1 + 10)

True

The solutions are

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

5 - 4 x - x = 0

\frac{2 x + 3}{x - 1} = x

2 x = 4

x + 1 = x + 13

x - 6 = 36 - 2 x

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(sqrt(10)-1),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(sqrt(10)-1),x=-3(1+sqrt(10))