3x^2+56x-24=0

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Solution for 3x^2+56x-24=0 equation:


Simplifying
3x2 + 56x + -24 = 0

Reorder the terms:
-24 + 56x + 3x2 = 0

Solving
-24 + 56x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-8 + 18.66666667x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 18.66666667x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 18.66666667x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 18.66666667x + x2 = 0 + 8
18.66666667x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
18.66666667x + x2 = 8

The x term is 18.66666667x.  Take half its coefficient (9.333333335).
Square it (87.11111114) and add it to both sides.

Add '87.11111114' to each side of the equation.
18.66666667x + 87.11111114 + x2 = 8 + 87.11111114

Reorder the terms:
87.11111114 + 18.66666667x + x2 = 8 + 87.11111114

Combine like terms: 8 + 87.11111114 = 95.11111114
87.11111114 + 18.66666667x + x2 = 95.11111114

Factor a perfect square on the left side:
(x + 9.333333335)(x + 9.333333335) = 95.11111114

Calculate the square root of the right side: 9.75249256

Break this problem into two subproblems by setting 
(x + 9.333333335) equal to 9.75249256 and -9.75249256.


Subproblem 1
x + 9.333333335 = 9.75249256

Simplifying
x + 9.333333335 = 9.75249256

Reorder the terms:
9.333333335 + x = 9.75249256

Solving
9.333333335 + x = 9.75249256

Solving for variable 'x'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + x = 9.75249256 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = 9.75249256 + -9.333333335
x = 9.75249256 + -9.333333335

Combine like terms: 9.75249256 + -9.333333335 = 0.419159225
x = 0.419159225

Simplifying
x = 0.419159225


Subproblem 2
x + 9.333333335 = -9.75249256

Simplifying
x + 9.333333335 = -9.75249256

Reorder the terms:
9.333333335 + x = -9.75249256

Solving
9.333333335 + x = -9.75249256

Solving for variable 'x'.

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

Add '-9.333333335' to each side of the equation.
9.333333335 + -9.333333335 + x = -9.75249256 + -9.333333335

Combine like terms: 9.333333335 + -9.333333335 = 0.000000000
0.000000000 + x = -9.75249256 + -9.333333335
x = -9.75249256 + -9.333333335

Combine like terms: -9.75249256 + -9.333333335 = -19.085825895
x = -19.085825895

Simplifying
x = -19.085825895


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.419159225, -19.085825895}

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