3x^2+24x-114=0

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Solution for 3x^2+24x-114=0 equation: 


Simplifying
3x2 + 24x + -114 = 0

Reorder the terms:
-114 + 24x + 3x2 = 0

Solving
-114 + 24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-38 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-38 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-38 + 8x + x2 = 0

Solving
-38 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 8x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 8x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 8x + x2 = 0 + 38
8x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
8x + x2 = 38

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 38 + 16

Reorder the terms:
16 + 8x + x2 = 38 + 16

Combine like terms: 38 + 16 = 54
16 + 8x + x2 = 54

Factor a perfect square on the left side:
(x + 4)(x + 4) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 4) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + 4 = 7.348469228

Simplifying
x + 4 = 7.348469228

Reorder the terms:
4 + x = 7.348469228

Solving
4 + x = 7.348469228

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.348469228 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.348469228 + -4
x = 7.348469228 + -4

Combine like terms: 7.348469228 + -4 = 3.348469228
x = 3.348469228

Simplifying
x = 3.348469228


Subproblem 2
x + 4 = -7.348469228

Simplifying
x + 4 = -7.348469228

Reorder the terms:
4 + x = -7.348469228

Solving
4 + x = -7.348469228

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.348469228 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.348469228 + -4
x = -7.348469228 + -4

Combine like terms: -7.348469228 + -4 = -11.348469228
x = -11.348469228

Simplifying
x = -11.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.348469228, -11.348469228}
Solution
x = {3.348469228, -11.348469228}

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