8*x^2-24x-288=0

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Solution for 8*x^2-24x-288=0 equation: 


Simplifying
8x2 + -24x + -288 = 0

Reorder the terms:
-288 + -24x + 8x2 = 0

Solving
-288 + -24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-36 + -3x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-36 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + -3x + x2 = 0

Solving
-36 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -3x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -3x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -3x + x2 = 0 + 36
-3x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-3x + x2 = 36

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 = 36 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + -3x + x2 = 38.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + -1.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + -1.5 = 6.184658438

Simplifying
x + -1.5 = 6.184658438

Reorder the terms:
-1.5 + x = 6.184658438

Solving
-1.5 + x = 6.184658438

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 = 6.184658438 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 6.184658438 + 1.5
x = 6.184658438 + 1.5

Combine like terms: 6.184658438 + 1.5 = 7.684658438
x = 7.684658438

Simplifying
x = 7.684658438


Subproblem 2
x + -1.5 = -6.184658438

Simplifying
x + -1.5 = -6.184658438

Reorder the terms:
-1.5 + x = -6.184658438

Solving
-1.5 + x = -6.184658438

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 = -6.184658438 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -6.184658438 + 1.5
x = -6.184658438 + 1.5

Combine like terms: -6.184658438 + 1.5 = -4.684658438
x = -4.684658438

Simplifying
x = -4.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.684658438, -4.684658438}
Solution
x = {7.684658438, -4.684658438}

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