x^2-4x+4+x^2-30x+225=13

Solution for x^2-4x+4+x^2-30x+225=13 equation:

Simplifying
x2 + -4x + 4 + x2 + -30x + 225 = 13

Reorder the terms:
4 + 225 + -4x + -30x + x2 + x2 = 13

Combine like terms: 4 + 225 = 229
229 + -4x + -30x + x2 + x2 = 13

Combine like terms: -4x + -30x = -34x
229 + -34x + x2 + x2 = 13

Combine like terms: x2 + x2 = 2x2
229 + -34x + 2x2 = 13

Solving
229 + -34x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
229 + -13 + -34x + 2x2 = 13 + -13

Combine like terms: 229 + -13 = 216
216 + -34x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
216 + -34x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + -17x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(108 + -17x + x2)' equal to zero and attempt to solve:

Simplifying
108 + -17x + x2 = 0

Solving
108 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + -17x + -108 + x2 = 0 + -108

Reorder the terms:
108 + -108 + -17x + x2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + -17x + x2 = 0 + -108
-17x + x2 = 0 + -108

Combine like terms: 0 + -108 = -108
-17x + x2 = -108

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -108 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -108 + 72.25

Combine like terms: -108 + 72.25 = -35.75
72.25 + -17x + x2 = -35.75

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = -35.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.