3x^2+24x+7=0

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Solution for 3x^2+24x+7=0 equation: 


Simplifying
3x2 + 24x + 7 = 0

Reorder the terms:
7 + 24x + 3x2 = 0

Solving
7 + 24x + 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'.
2.333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 8x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 8x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 8x + x2 = 0 + -2.333333333
8x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
8x + x2 = -2.333333333

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 = -2.333333333 + 16

Reorder the terms:
16 + 8x + x2 = -2.333333333 + 16

Combine like terms: -2.333333333 + 16 = 13.666666667
16 + 8x + x2 = 13.666666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 13.666666667

Calculate the square root of the right side: 3.696845502

Break this problem into two subproblems by setting 
(x + 4) equal to 3.696845502 and -3.696845502.


Subproblem 1
x + 4 = 3.696845502

Simplifying
x + 4 = 3.696845502

Reorder the terms:
4 + x = 3.696845502

Solving
4 + x = 3.696845502

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 = 3.696845502 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.696845502 + -4
x = 3.696845502 + -4

Combine like terms: 3.696845502 + -4 = -0.303154498
x = -0.303154498

Simplifying
x = -0.303154498


Subproblem 2
x + 4 = -3.696845502

Simplifying
x + 4 = -3.696845502

Reorder the terms:
4 + x = -3.696845502

Solving
4 + x = -3.696845502

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 = -3.696845502 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.696845502 + -4
x = -3.696845502 + -4

Combine like terms: -3.696845502 + -4 = -7.696845502
x = -7.696845502

Simplifying
x = -7.696845502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.303154498, -7.696845502}

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