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 = 405
256 + -32x + x2 = 405

Factor a perfect square on the left side:
(x + -16)(x + -16) = 405

Calculate the square root of the right side: 20.124611797

Break this problem into two subproblems by setting 
(x + -16) equal to 20.124611797 and -20.124611797.


Subproblem 1
x + -16 = 20.124611797

Simplifying
x + -16 = 20.124611797

Reorder the terms:
-16 + x = 20.124611797

Solving
-16 + x = 20.124611797

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 = 20.124611797 + 16

Combine like terms: -16 + 16 = 0
0 + x = 20.124611797 + 16
x = 20.124611797 + 16

Combine like terms: 20.124611797 + 16 = 36.124611797
x = 36.124611797

Simplifying
x = 36.124611797


Subproblem 2
x + -16 = -20.124611797

Simplifying
x + -16 = -20.124611797

Reorder the terms:
-16 + x = -20.124611797

Solving
-16 + x = -20.124611797

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 = -20.124611797 + 16

Combine like terms: -16 + 16 = 0
0 + x = -20.124611797 + 16
x = -20.124611797 + 16

Combine like terms: -20.124611797 + 16 = -4.124611797
x = -4.124611797

Simplifying
x = -4.124611797


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.124611797, -4.124611797}

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