x^2-32x+177=0

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Solution for x^2-32x+177=0 equation: 


Simplifying
x2 + -32x + 177 = 0

Reorder the terms:
177 + -32x + x2 = 0

Solving
177 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-177' to each side of the equation.
177 + -32x + -177 + x2 = 0 + -177

Reorder the terms:
177 + -177 + -32x + x2 = 0 + -177

Combine like terms: 177 + -177 = 0
0 + -32x + x2 = 0 + -177
-32x + x2 = 0 + -177

Combine like terms: 0 + -177 = -177
-32x + x2 = -177

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 = -177 + 256

Reorder the terms:
256 + -32x + x2 = -177 + 256

Combine like terms: -177 + 256 = 79
256 + -32x + x2 = 79

Factor a perfect square on the left side:
(x + -16)(x + -16) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + -16) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + -16 = 8.888194417

Simplifying
x + -16 = 8.888194417

Reorder the terms:
-16 + x = 8.888194417

Solving
-16 + x = 8.888194417

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 = 8.888194417 + 16

Combine like terms: -16 + 16 = 0
0 + x = 8.888194417 + 16
x = 8.888194417 + 16

Combine like terms: 8.888194417 + 16 = 24.888194417
x = 24.888194417

Simplifying
x = 24.888194417


Subproblem 2
x + -16 = -8.888194417

Simplifying
x + -16 = -8.888194417

Reorder the terms:
-16 + x = -8.888194417

Solving
-16 + x = -8.888194417

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 = -8.888194417 + 16

Combine like terms: -16 + 16 = 0
0 + x = -8.888194417 + 16
x = -8.888194417 + 16

Combine like terms: -8.888194417 + 16 = 7.111805583
x = 7.111805583

Simplifying
x = 7.111805583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.888194417, 7.111805583}

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