x^2+32x-60=0

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Solution for x^2+32x-60=0 equation: 


Simplifying
x2 + 32x + -60 = 0

Reorder the terms:
-60 + 32x + x2 = 0

Solving
-60 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 32x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 32x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 32x + x2 = 0 + 60
32x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
32x + x2 = 60

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 = 60 + 256

Reorder the terms:
256 + 32x + x2 = 60 + 256

Combine like terms: 60 + 256 = 316
256 + 32x + x2 = 316

Factor a perfect square on the left side:
(x + 16)(x + 16) = 316

Calculate the square root of the right side: 17.776388835

Break this problem into two subproblems by setting 
(x + 16) equal to 17.776388835 and -17.776388835.


Subproblem 1
x + 16 = 17.776388835

Simplifying
x + 16 = 17.776388835

Reorder the terms:
16 + x = 17.776388835

Solving
16 + x = 17.776388835

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 = 17.776388835 + -16

Combine like terms: 16 + -16 = 0
0 + x = 17.776388835 + -16
x = 17.776388835 + -16

Combine like terms: 17.776388835 + -16 = 1.776388835
x = 1.776388835

Simplifying
x = 1.776388835


Subproblem 2
x + 16 = -17.776388835

Simplifying
x + 16 = -17.776388835

Reorder the terms:
16 + x = -17.776388835

Solving
16 + x = -17.776388835

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 = -17.776388835 + -16

Combine like terms: 16 + -16 = 0
0 + x = -17.776388835 + -16
x = -17.776388835 + -16

Combine like terms: -17.776388835 + -16 = -33.776388835
x = -33.776388835

Simplifying
x = -33.776388835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.776388835, -33.776388835}

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