(x^2)+32x-135=0

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Solution for (x^2)+32x-135=0 equation: 


Simplifying
(x2) + 32x + -135 = 0
x2 + 32x + -135 = 0

Reorder the terms:
-135 + 32x + x2 = 0

Solving
-135 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + 32x + 135 + x2 = 0 + 135

Reorder the terms:
-135 + 135 + 32x + x2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + 32x + x2 = 0 + 135
32x + x2 = 0 + 135

Combine like terms: 0 + 135 = 135
32x + x2 = 135

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 = 135 + 256

Reorder the terms:
256 + 32x + x2 = 135 + 256

Combine like terms: 135 + 256 = 391
256 + 32x + x2 = 391

Factor a perfect square on the left side:
(x + 16)(x + 16) = 391

Calculate the square root of the right side: 19.773719933

Break this problem into two subproblems by setting 
(x + 16) equal to 19.773719933 and -19.773719933.


Subproblem 1
x + 16 = 19.773719933

Simplifying
x + 16 = 19.773719933

Reorder the terms:
16 + x = 19.773719933

Solving
16 + x = 19.773719933

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 = 19.773719933 + -16

Combine like terms: 16 + -16 = 0
0 + x = 19.773719933 + -16
x = 19.773719933 + -16

Combine like terms: 19.773719933 + -16 = 3.773719933
x = 3.773719933

Simplifying
x = 3.773719933


Subproblem 2
x + 16 = -19.773719933

Simplifying
x + 16 = -19.773719933

Reorder the terms:
16 + x = -19.773719933

Solving
16 + x = -19.773719933

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 = -19.773719933 + -16

Combine like terms: 16 + -16 = 0
0 + x = -19.773719933 + -16
x = -19.773719933 + -16

Combine like terms: -19.773719933 + -16 = -35.773719933
x = -35.773719933

Simplifying
x = -35.773719933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.773719933, -35.773719933}

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