100x^2+132x+40=0

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Solution for 100x^2+132x+40=0 equation: 


Simplifying
100x2 + 132x + 40 = 0

Reorder the terms:
40 + 132x + 100x2 = 0

Solving
40 + 132x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + 33x + 25x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(10 + 33x + 25x2)' equal to zero and attempt to solve:

Simplifying
10 + 33x + 25x2 = 0

Solving
10 + 33x + 25x2 = 0

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

Divide each side by '25'.
0.4 + 1.32x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.32x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.32x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.32x + x2 = 0 + -0.4
1.32x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.32x + x2 = -0.4

The x term is 1.32x.  Take half its coefficient (0.66).
Square it (0.4356) and add it to both sides.

Add '0.4356' to each side of the equation.
1.32x + 0.4356 + x2 = -0.4 + 0.4356

Reorder the terms:
0.4356 + 1.32x + x2 = -0.4 + 0.4356

Combine like terms: -0.4 + 0.4356 = 0.0356
0.4356 + 1.32x + x2 = 0.0356

Factor a perfect square on the left side:
(x + 0.66)(x + 0.66) = 0.0356

Calculate the square root of the right side: 0.188679623

Break this problem into two subproblems by setting 
(x + 0.66) equal to 0.188679623 and -0.188679623.


Subproblem 1
x + 0.66 = 0.188679623

Simplifying
x + 0.66 = 0.188679623

Reorder the terms:
0.66 + x = 0.188679623

Solving
0.66 + x = 0.188679623

Solving for variable 'x'.

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

Add '-0.66' to each side of the equation.
0.66 + -0.66 + x = 0.188679623 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
0.00 + x = 0.188679623 + -0.66
x = 0.188679623 + -0.66

Combine like terms: 0.188679623 + -0.66 = -0.471320377
x = -0.471320377

Simplifying
x = -0.471320377


Subproblem 2
x + 0.66 = -0.188679623

Simplifying
x + 0.66 = -0.188679623

Reorder the terms:
0.66 + x = -0.188679623

Solving
0.66 + x = -0.188679623

Solving for variable 'x'.

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

Add '-0.66' to each side of the equation.
0.66 + -0.66 + x = -0.188679623 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
0.00 + x = -0.188679623 + -0.66
x = -0.188679623 + -0.66

Combine like terms: -0.188679623 + -0.66 = -0.848679623
x = -0.848679623

Simplifying
x = -0.848679623


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.471320377, -0.848679623}
Solution
x = {-0.471320377, -0.848679623}

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