40x^2+12x-238=0

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Solution for 40x^2+12x-238=0 equation: 


Simplifying
40x2 + 12x + -238 = 0

Reorder the terms:
-238 + 12x + 40x2 = 0

Solving
-238 + 12x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-119 + 6x + 20x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-119 + 6x + 20x2)' equal to zero and attempt to solve:

Simplifying
-119 + 6x + 20x2 = 0

Solving
-119 + 6x + 20x2 = 0

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

Divide each side by '20'.
-5.95 + 0.3x + x2 = 0.0

Move the constant term to the right:

Add '5.95' to each side of the equation.
-5.95 + 0.3x + 5.95 + x2 = 0.0 + 5.95

Reorder the terms:
-5.95 + 5.95 + 0.3x + x2 = 0.0 + 5.95

Combine like terms: -5.95 + 5.95 = 0.00
0.00 + 0.3x + x2 = 0.0 + 5.95
0.3x + x2 = 0.0 + 5.95

Combine like terms: 0.0 + 5.95 = 5.95
0.3x + x2 = 5.95

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 5.95 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 5.95 + 0.0225

Combine like terms: 5.95 + 0.0225 = 5.9725
0.0225 + 0.3x + x2 = 5.9725

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 5.9725

Calculate the square root of the right side: 2.443869882

Break this problem into two subproblems by setting 
(x + 0.15) equal to 2.443869882 and -2.443869882.


Subproblem 1
x + 0.15 = 2.443869882

Simplifying
x + 0.15 = 2.443869882

Reorder the terms:
0.15 + x = 2.443869882

Solving
0.15 + x = 2.443869882

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 2.443869882 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 2.443869882 + -0.15
x = 2.443869882 + -0.15

Combine like terms: 2.443869882 + -0.15 = 2.293869882
x = 2.293869882

Simplifying
x = 2.293869882


Subproblem 2
x + 0.15 = -2.443869882

Simplifying
x + 0.15 = -2.443869882

Reorder the terms:
0.15 + x = -2.443869882

Solving
0.15 + x = -2.443869882

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -2.443869882 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -2.443869882 + -0.15
x = -2.443869882 + -0.15

Combine like terms: -2.443869882 + -0.15 = -2.593869882
x = -2.593869882

Simplifying
x = -2.593869882


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.293869882, -2.593869882}
Solution
x = {2.293869882, -2.593869882}

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