18x^2+126x+15=0

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Solution for 18x^2+126x+15=0 equation: 


Simplifying
18x2 + 126x + 15 = 0

Reorder the terms:
15 + 126x + 18x2 = 0

Solving
15 + 126x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 42x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 42x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 42x + 6x2 = 0

Solving
5 + 42x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 7x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 7x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 7x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 7x + x2 = 0 + -0.8333333333
7x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
7x + x2 = -0.8333333333

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -0.8333333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -0.8333333333 + 12.25

Combine like terms: -0.8333333333 + 12.25 = 11.4166666667
12.25 + 7x + x2 = 11.4166666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 11.4166666667

Calculate the square root of the right side: 3.378855822

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.378855822 and -3.378855822.


Subproblem 1
x + 3.5 = 3.378855822

Simplifying
x + 3.5 = 3.378855822

Reorder the terms:
3.5 + x = 3.378855822

Solving
3.5 + x = 3.378855822

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.378855822 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.378855822 + -3.5
x = 3.378855822 + -3.5

Combine like terms: 3.378855822 + -3.5 = -0.121144178
x = -0.121144178

Simplifying
x = -0.121144178


Subproblem 2
x + 3.5 = -3.378855822

Simplifying
x + 3.5 = -3.378855822

Reorder the terms:
3.5 + x = -3.378855822

Solving
3.5 + x = -3.378855822

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.378855822 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.378855822 + -3.5
x = -3.378855822 + -3.5

Combine like terms: -3.378855822 + -3.5 = -6.878855822
x = -6.878855822

Simplifying
x = -6.878855822


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.121144178, -6.878855822}
Solution
x = {-0.121144178, -6.878855822}

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