3x^2+28x+24=0

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Solution for 3x^2+28x+24=0 equation: 


Simplifying
3x2 + 28x + 24 = 0

Reorder the terms:
24 + 28x + 3x2 = 0

Solving
24 + 28x + 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 + 9.333333333x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 9.333333333x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 9.333333333x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 9.333333333x + x2 = 0 + -8
9.333333333x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
9.333333333x + x2 = -8

The x term is 9.333333333x.  Take half its coefficient (4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
9.333333333x + 21.77777778 + x2 = -8 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333x + x2 = -8 + 21.77777778

Combine like terms: -8 + 21.77777778 = 13.77777778
21.77777778 + 9.333333333x + x2 = 13.77777778

Factor a perfect square on the left side:
(x + 4.666666667)(x + 4.666666667) = 13.77777778

Calculate the square root of the right side: 3.711842909

Break this problem into two subproblems by setting 
(x + 4.666666667) equal to 3.711842909 and -3.711842909.


Subproblem 1
x + 4.666666667 = 3.711842909

Simplifying
x + 4.666666667 = 3.711842909

Reorder the terms:
4.666666667 + x = 3.711842909

Solving
4.666666667 + x = 3.711842909

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x = 3.711842909 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = 3.711842909 + -4.666666667
x = 3.711842909 + -4.666666667

Combine like terms: 3.711842909 + -4.666666667 = -0.954823758
x = -0.954823758

Simplifying
x = -0.954823758


Subproblem 2
x + 4.666666667 = -3.711842909

Simplifying
x + 4.666666667 = -3.711842909

Reorder the terms:
4.666666667 + x = -3.711842909

Solving
4.666666667 + x = -3.711842909

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x = -3.711842909 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = -3.711842909 + -4.666666667
x = -3.711842909 + -4.666666667

Combine like terms: -3.711842909 + -4.666666667 = -8.378509576
x = -8.378509576

Simplifying
x = -8.378509576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.954823758, -8.378509576}

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