18x^2+24x+5=0

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Solution for 18x^2+24x+5=0 equation: 


Simplifying
18x2 + 24x + 5 = 0

Reorder the terms:
5 + 24x + 18x2 = 0

Solving
5 + 24x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
0.2777777778 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-0.2777777778' to each side of the equation.
0.2777777778 + 1.333333333x + -0.2777777778 + x2 = 0 + -0.2777777778

Reorder the terms:
0.2777777778 + -0.2777777778 + 1.333333333x + x2 = 0 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + 1.333333333x + x2 = 0 + -0.2777777778
1.333333333x + x2 = 0 + -0.2777777778

Combine like terms: 0 + -0.2777777778 = -0.2777777778
1.333333333x + x2 = -0.2777777778

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = -0.2777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -0.2777777778 + 0.4444444442

Combine like terms: -0.2777777778 + 0.4444444442 = 0.1666666664
0.4444444442 + 1.333333333x + x2 = 0.1666666664

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 0.1666666664

Calculate the square root of the right side: 0.40824829

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 0.40824829 and -0.40824829.


Subproblem 1
x + 0.6666666665 = 0.40824829

Simplifying
x + 0.6666666665 = 0.40824829

Reorder the terms:
0.6666666665 + x = 0.40824829

Solving
0.6666666665 + x = 0.40824829

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 0.40824829 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 0.40824829 + -0.6666666665
x = 0.40824829 + -0.6666666665

Combine like terms: 0.40824829 + -0.6666666665 = -0.2584183765
x = -0.2584183765

Simplifying
x = -0.2584183765


Subproblem 2
x + 0.6666666665 = -0.40824829

Simplifying
x + 0.6666666665 = -0.40824829

Reorder the terms:
0.6666666665 + x = -0.40824829

Solving
0.6666666665 + x = -0.40824829

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -0.40824829 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -0.40824829 + -0.6666666665
x = -0.40824829 + -0.6666666665

Combine like terms: -0.40824829 + -0.6666666665 = -1.0749149565
x = -1.0749149565

Simplifying
x = -1.0749149565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2584183765, -1.0749149565}

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