3x^2+24x+5=0

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Solution for 3x^2+24x+5=0 equation: 


Simplifying
3x2 + 24x + 5 = 0

Reorder the terms:
5 + 24x + 3x2 = 0

Solving
5 + 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'.
1.666666667 + 8x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 8x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 8x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 8x + x2 = 0 + -1.666666667
8x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
8x + x2 = -1.666666667

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 = -1.666666667 + 16

Reorder the terms:
16 + 8x + x2 = -1.666666667 + 16

Combine like terms: -1.666666667 + 16 = 14.333333333
16 + 8x + x2 = 14.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 14.333333333

Calculate the square root of the right side: 3.785938897

Break this problem into two subproblems by setting 
(x + 4) equal to 3.785938897 and -3.785938897.


Subproblem 1
x + 4 = 3.785938897

Simplifying
x + 4 = 3.785938897

Reorder the terms:
4 + x = 3.785938897

Solving
4 + x = 3.785938897

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 = 3.785938897 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.785938897 + -4
x = 3.785938897 + -4

Combine like terms: 3.785938897 + -4 = -0.214061103
x = -0.214061103

Simplifying
x = -0.214061103


Subproblem 2
x + 4 = -3.785938897

Simplifying
x + 4 = -3.785938897

Reorder the terms:
4 + x = -3.785938897

Solving
4 + x = -3.785938897

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 = -3.785938897 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.785938897 + -4
x = -3.785938897 + -4

Combine like terms: -3.785938897 + -4 = -7.785938897
x = -7.785938897

Simplifying
x = -7.785938897


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.214061103, -7.785938897}

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