8x^2-68x-60=0

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Solution for 8x^2-68x-60=0 equation: 


Simplifying
8x2 + -68x + -60 = 0

Reorder the terms:
-60 + -68x + 8x2 = 0

Solving
-60 + -68x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -17x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + -17x + 2x2)' equal to zero and attempt to solve:

Simplifying
-15 + -17x + 2x2 = 0

Solving
-15 + -17x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-7.5 + -8.5x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -8.5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -8.5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -8.5x + x2 = 0 + 7.5
-8.5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-8.5x + x2 = 7.5

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 7.5 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 7.5 + 18.0625

Combine like terms: 7.5 + 18.0625 = 25.5625
18.0625 + -8.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + -4.25) equal to 5.055937104 and -5.055937104.


Subproblem 1
x + -4.25 = 5.055937104

Simplifying
x + -4.25 = 5.055937104

Reorder the terms:
-4.25 + x = 5.055937104

Solving
-4.25 + x = 5.055937104

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 5.055937104 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 5.055937104 + 4.25
x = 5.055937104 + 4.25

Combine like terms: 5.055937104 + 4.25 = 9.305937104
x = 9.305937104

Simplifying
x = 9.305937104


Subproblem 2
x + -4.25 = -5.055937104

Simplifying
x + -4.25 = -5.055937104

Reorder the terms:
-4.25 + x = -5.055937104

Solving
-4.25 + x = -5.055937104

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -5.055937104 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -5.055937104 + 4.25
x = -5.055937104 + 4.25

Combine like terms: -5.055937104 + 4.25 = -0.805937104
x = -0.805937104

Simplifying
x = -0.805937104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.305937104, -0.805937104}
Solution
x = {9.305937104, -0.805937104}

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