x^2+x^2=(18-2x)*(18-2x)

Solution for x^2+x^2=(18-2x)*(18-2x) equation:

Simplifying
x2 + x2 = (18 + -2x)(18 + -2x)

Combine like terms: x2 + x2 = 2x2
2x2 = (18 + -2x)(18 + -2x)

Multiply (18 + -2x) * (18 + -2x)
2x2 = (18(18 + -2x) + -2x * (18 + -2x))
2x2 = ((18 * 18 + -2x * 18) + -2x * (18 + -2x))
2x2 = ((324 + -36x) + -2x * (18 + -2x))
2x2 = (324 + -36x + (18 * -2x + -2x * -2x))
2x2 = (324 + -36x + (-36x + 4x2))

Combine like terms: -36x + -36x = -72x
2x2 = (324 + -72x + 4x2)

Solving
2x2 = 324 + -72x + 4x2

Solving for variable 'x'.

Reorder the terms:
-324 + 72x + 2x2 + -4x2 = 324 + -72x + 4x2 + -324 + 72x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-324 + 72x + -2x2 = 324 + -72x + 4x2 + -324 + 72x + -4x2

Reorder the terms:
-324 + 72x + -2x2 = 324 + -324 + -72x + 72x + 4x2 + -4x2

Combine like terms: 324 + -324 = 0
-324 + 72x + -2x2 = 0 + -72x + 72x + 4x2 + -4x2
-324 + 72x + -2x2 = -72x + 72x + 4x2 + -4x2

Combine like terms: -72x + 72x = 0
-324 + 72x + -2x2 = 0 + 4x2 + -4x2
-324 + 72x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-324 + 72x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-162 + 36x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-162 + 36x + -1x2)' equal to zero and attempt to solve:

Simplifying
-162 + 36x + -1x2 = 0

Solving
-162 + 36x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
162 + -36x + x2 = 0

Move the constant term to the right:

Add '-162' to each side of the equation.
162 + -36x + -162 + x2 = 0 + -162

Reorder the terms:
162 + -162 + -36x + x2 = 0 + -162

Combine like terms: 162 + -162 = 0
0 + -36x + x2 = 0 + -162
-36x + x2 = 0 + -162

Combine like terms: 0 + -162 = -162
-36x + x2 = -162

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -162 + 324

Reorder the terms:
324 + -36x + x2 = -162 + 324

Combine like terms: -162 + 324 = 162
324 + -36x + x2 = 162

Factor a perfect square on the left side:
(x + -18)(x + -18) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(x + -18) equal to 12.727922061 and -12.727922061.

Subproblem 1
x + -18 = 12.727922061

Simplifying
x + -18 = 12.727922061

Reorder the terms:
-18 + x = 12.727922061

Solving
-18 + x = 12.727922061

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '18' to each side of the equation.
-18 + 18 + x = 12.727922061 + 18

Combine like terms: -18 + 18 = 0
0 + x = 12.727922061 + 18
x = 12.727922061 + 18

Combine like terms: 12.727922061 + 18 = 30.727922061
x = 30.727922061

Simplifying
x = 30.727922061

Subproblem 2
x + -18 = -12.727922061

Simplifying
x + -18 = -12.727922061

Reorder the terms:
-18 + x = -12.727922061

Solving
-18 + x = -12.727922061

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '18' to each side of the equation.
-18 + 18 + x = -12.727922061 + 18

Combine like terms: -18 + 18 = 0
0 + x = -12.727922061 + 18
x = -12.727922061 + 18

Combine like terms: -12.727922061 + 18 = 5.272077939
x = 5.272077939

Simplifying
x = 5.272077939

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.727922061, 5.272077939}
Solution
x = {30.727922061, 5.272077939}