x^2-32x+256-37=0

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Solution for x^2-32x+256-37=0 equation: 


Simplifying
x2 + -32x + 256 + -37 = 0

Reorder the terms:
256 + -37 + -32x + x2 = 0

Combine like terms: 256 + -37 = 219
219 + -32x + x2 = 0

Solving
219 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-219' to each side of the equation.
219 + -32x + -219 + x2 = 0 + -219

Reorder the terms:
219 + -219 + -32x + x2 = 0 + -219

Combine like terms: 219 + -219 = 0
0 + -32x + x2 = 0 + -219
-32x + x2 = 0 + -219

Combine like terms: 0 + -219 = -219
-32x + x2 = -219

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -219 + 256

Reorder the terms:
256 + -32x + x2 = -219 + 256

Combine like terms: -219 + 256 = 37
256 + -32x + x2 = 37

Factor a perfect square on the left side:
(x + -16)(x + -16) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -16) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + -16 = 6.08276253

Simplifying
x + -16 = 6.08276253

Reorder the terms:
-16 + x = 6.08276253

Solving
-16 + x = 6.08276253

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = 6.08276253 + 16

Combine like terms: -16 + 16 = 0
0 + x = 6.08276253 + 16
x = 6.08276253 + 16

Combine like terms: 6.08276253 + 16 = 22.08276253
x = 22.08276253

Simplifying
x = 22.08276253


Subproblem 2
x + -16 = -6.08276253

Simplifying
x + -16 = -6.08276253

Reorder the terms:
-16 + x = -6.08276253

Solving
-16 + x = -6.08276253

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = -6.08276253 + 16

Combine like terms: -16 + 16 = 0
0 + x = -6.08276253 + 16
x = -6.08276253 + 16

Combine like terms: -6.08276253 + 16 = 9.91723747
x = 9.91723747

Simplifying
x = 9.91723747


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.08276253, 9.91723747}

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