2x^2+16x-60=0

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Solution for 2x^2+16x-60=0 equation: 


Simplifying
2x2 + 16x + -60 = 0

Reorder the terms:
-60 + 16x + 2x2 = 0

Solving
-60 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 8x + x2 = 0

Solving
-30 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 8x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 8x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 8x + x2 = 0 + 30
8x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
8x + x2 = 30

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 30 + 16

Reorder the terms:
16 + 8x + x2 = 30 + 16

Combine like terms: 30 + 16 = 46
16 + 8x + x2 = 46

Factor a perfect square on the left side:
(x + 4)(x + 4) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 4) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + 4 = 6.782329983

Simplifying
x + 4 = 6.782329983

Reorder the terms:
4 + x = 6.782329983

Solving
4 + x = 6.782329983

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.782329983 + -4
x = 6.782329983 + -4

Combine like terms: 6.782329983 + -4 = 2.782329983
x = 2.782329983

Simplifying
x = 2.782329983


Subproblem 2
x + 4 = -6.782329983

Simplifying
x + 4 = -6.782329983

Reorder the terms:
4 + x = -6.782329983

Solving
4 + x = -6.782329983

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = -6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.782329983 + -4
x = -6.782329983 + -4

Combine like terms: -6.782329983 + -4 = -10.782329983
x = -10.782329983

Simplifying
x = -10.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.782329983, -10.782329983}
Solution
x = {2.782329983, -10.782329983}

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