8x^2+36x-288=0

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Solution for 8x^2+36x-288=0 equation: 


Simplifying
8x2 + 36x + -288 = 0

Reorder the terms:
-288 + 36x + 8x2 = 0

Solving
-288 + 36x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 9x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-72 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-72 + 9x + 2x2 = 0

Solving
-72 + 9x + 2x2 = 0

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

Divide each side by '2'.
-36 + 4.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 4.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 4.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4.5x + x2 = 0 + 36
4.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
4.5x + x2 = 36

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 36 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 36 + 5.0625

Combine like terms: 36 + 5.0625 = 41.0625
5.0625 + 4.5x + x2 = 41.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 41.0625

Calculate the square root of the right side: 6.408002809

Break this problem into two subproblems by setting 
(x + 2.25) equal to 6.408002809 and -6.408002809.


Subproblem 1
x + 2.25 = 6.408002809

Simplifying
x + 2.25 = 6.408002809

Reorder the terms:
2.25 + x = 6.408002809

Solving
2.25 + x = 6.408002809

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 6.408002809 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 6.408002809 + -2.25
x = 6.408002809 + -2.25

Combine like terms: 6.408002809 + -2.25 = 4.158002809
x = 4.158002809

Simplifying
x = 4.158002809


Subproblem 2
x + 2.25 = -6.408002809

Simplifying
x + 2.25 = -6.408002809

Reorder the terms:
2.25 + x = -6.408002809

Solving
2.25 + x = -6.408002809

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -6.408002809 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -6.408002809 + -2.25
x = -6.408002809 + -2.25

Combine like terms: -6.408002809 + -2.25 = -8.658002809
x = -8.658002809

Simplifying
x = -8.658002809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.158002809, -8.658002809}
Solution
x = {4.158002809, -8.658002809}

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