4x^2+102x+288=0

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Solution for 4x^2+102x+288=0 equation: 


Simplifying
4x2 + 102x + 288 = 0

Reorder the terms:
288 + 102x + 4x2 = 0

Solving
288 + 102x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(144 + 51x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(144 + 51x + 2x2)' equal to zero and attempt to solve:

Simplifying
144 + 51x + 2x2 = 0

Solving
144 + 51x + 2x2 = 0

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

Divide each side by '2'.
72 + 25.5x + x2 = 0

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + 25.5x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + 25.5x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + 25.5x + x2 = 0 + -72
25.5x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
25.5x + x2 = -72

The x term is 25.5x.  Take half its coefficient (12.75).
Square it (162.5625) and add it to both sides.

Add '162.5625' to each side of the equation.
25.5x + 162.5625 + x2 = -72 + 162.5625

Reorder the terms:
162.5625 + 25.5x + x2 = -72 + 162.5625

Combine like terms: -72 + 162.5625 = 90.5625
162.5625 + 25.5x + x2 = 90.5625

Factor a perfect square on the left side:
(x + 12.75)(x + 12.75) = 90.5625

Calculate the square root of the right side: 9.516433155

Break this problem into two subproblems by setting 
(x + 12.75) equal to 9.516433155 and -9.516433155.


Subproblem 1
x + 12.75 = 9.516433155

Simplifying
x + 12.75 = 9.516433155

Reorder the terms:
12.75 + x = 9.516433155

Solving
12.75 + x = 9.516433155

Solving for variable 'x'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + x = 9.516433155 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + x = 9.516433155 + -12.75
x = 9.516433155 + -12.75

Combine like terms: 9.516433155 + -12.75 = -3.233566845
x = -3.233566845

Simplifying
x = -3.233566845


Subproblem 2
x + 12.75 = -9.516433155

Simplifying
x + 12.75 = -9.516433155

Reorder the terms:
12.75 + x = -9.516433155

Solving
12.75 + x = -9.516433155

Solving for variable 'x'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + x = -9.516433155 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + x = -9.516433155 + -12.75
x = -9.516433155 + -12.75

Combine like terms: -9.516433155 + -12.75 = -22.266433155
x = -22.266433155

Simplifying
x = -22.266433155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.233566845, -22.266433155}
Solution
x = {-3.233566845, -22.266433155}

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