x^2-32x+149=0

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Solution for x^2-32x+149=0 equation: 


Simplifying
x2 + -32x + 149 = 0

Reorder the terms:
149 + -32x + x2 = 0

Solving
149 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-149' to each side of the equation.
149 + -32x + -149 + x2 = 0 + -149

Reorder the terms:
149 + -149 + -32x + x2 = 0 + -149

Combine like terms: 149 + -149 = 0
0 + -32x + x2 = 0 + -149
-32x + x2 = 0 + -149

Combine like terms: 0 + -149 = -149
-32x + x2 = -149

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 = -149 + 256

Reorder the terms:
256 + -32x + x2 = -149 + 256

Combine like terms: -149 + 256 = 107
256 + -32x + x2 = 107

Factor a perfect square on the left side:
(x + -16)(x + -16) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(x + -16) equal to 10.344080433 and -10.344080433.


Subproblem 1
x + -16 = 10.344080433

Simplifying
x + -16 = 10.344080433

Reorder the terms:
-16 + x = 10.344080433

Solving
-16 + x = 10.344080433

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 = 10.344080433 + 16

Combine like terms: -16 + 16 = 0
0 + x = 10.344080433 + 16
x = 10.344080433 + 16

Combine like terms: 10.344080433 + 16 = 26.344080433
x = 26.344080433

Simplifying
x = 26.344080433


Subproblem 2
x + -16 = -10.344080433

Simplifying
x + -16 = -10.344080433

Reorder the terms:
-16 + x = -10.344080433

Solving
-16 + x = -10.344080433

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 = -10.344080433 + 16

Combine like terms: -16 + 16 = 0
0 + x = -10.344080433 + 16
x = -10.344080433 + 16

Combine like terms: -10.344080433 + 16 = 5.655919567
x = 5.655919567

Simplifying
x = 5.655919567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.344080433, 5.655919567}

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