4x^2+64x-60=0

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Solution for 4x^2+64x-60=0 equation: 


Simplifying
4x2 + 64x + -60 = 0

Reorder the terms:
-60 + 64x + 4x2 = 0

Solving
-60 + 64x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 16x + x2 = 0

Solving
-15 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 16x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 16x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 16x + x2 = 0 + 15
16x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
16x + x2 = 15

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 15 + 64

Reorder the terms:
64 + 16x + x2 = 15 + 64

Combine like terms: 15 + 64 = 79
64 + 16x + x2 = 79

Factor a perfect square on the left side:
(x + 8)(x + 8) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + 8) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + 8 = 8.888194417

Simplifying
x + 8 = 8.888194417

Reorder the terms:
8 + x = 8.888194417

Solving
8 + x = 8.888194417

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 8.888194417 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.888194417 + -8
x = 8.888194417 + -8

Combine like terms: 8.888194417 + -8 = 0.888194417
x = 0.888194417

Simplifying
x = 0.888194417


Subproblem 2
x + 8 = -8.888194417

Simplifying
x + 8 = -8.888194417

Reorder the terms:
8 + x = -8.888194417

Solving
8 + x = -8.888194417

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -8.888194417 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.888194417 + -8
x = -8.888194417 + -8

Combine like terms: -8.888194417 + -8 = -16.888194417
x = -16.888194417

Simplifying
x = -16.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.888194417, -16.888194417}
Solution
x = {0.888194417, -16.888194417}

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