8x^2+24x-768=0

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Solution for 8x^2+24x-768=0 equation: 


Simplifying
8x2 + 24x + -768 = 0

Reorder the terms:
-768 + 24x + 8x2 = 0

Solving
-768 + 24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-96 + 3x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-96 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + 3x + x2 = 0

Solving
-96 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 3x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 3x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 3x + x2 = 0 + 96
3x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
3x + x2 = 96

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 96 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 96 + 2.25

Combine like terms: 96 + 2.25 = 98.25
2.25 + 3x + x2 = 98.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(x + 1.5) equal to 9.912113801 and -9.912113801.


Subproblem 1
x + 1.5 = 9.912113801

Simplifying
x + 1.5 = 9.912113801

Reorder the terms:
1.5 + x = 9.912113801

Solving
1.5 + x = 9.912113801

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 9.912113801 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 9.912113801 + -1.5
x = 9.912113801 + -1.5

Combine like terms: 9.912113801 + -1.5 = 8.412113801
x = 8.412113801

Simplifying
x = 8.412113801


Subproblem 2
x + 1.5 = -9.912113801

Simplifying
x + 1.5 = -9.912113801

Reorder the terms:
1.5 + x = -9.912113801

Solving
1.5 + x = -9.912113801

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -9.912113801 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -9.912113801 + -1.5
x = -9.912113801 + -1.5

Combine like terms: -9.912113801 + -1.5 = -11.412113801
x = -11.412113801

Simplifying
x = -11.412113801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.412113801, -11.412113801}
Solution
x = {8.412113801, -11.412113801}

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