15x^2+13x-4=0

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Solution for 15x^2+13x-4=0 equation: 


Simplifying
15x2 + 13x + -4 = 0

Reorder the terms:
-4 + 13x + 15x2 = 0

Solving
-4 + 13x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.2666666667 + 0.8666666667x + x2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + 0.8666666667x + 0.2666666667 + x2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + 0.8666666667x + x2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + 0.8666666667x + x2 = 0 + 0.2666666667
0.8666666667x + x2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
0.8666666667x + x2 = 0.2666666667

The x term is 0.8666666667x.  Take half its coefficient (0.4333333334).
Square it (0.1877777778) and add it to both sides.

Add '0.1877777778' to each side of the equation.
0.8666666667x + 0.1877777778 + x2 = 0.2666666667 + 0.1877777778

Reorder the terms:
0.1877777778 + 0.8666666667x + x2 = 0.2666666667 + 0.1877777778

Combine like terms: 0.2666666667 + 0.1877777778 = 0.4544444445
0.1877777778 + 0.8666666667x + x2 = 0.4544444445

Factor a perfect square on the left side:
(x + 0.4333333334)(x + 0.4333333334) = 0.4544444445

Calculate the square root of the right side: 0.674124947

Break this problem into two subproblems by setting 
(x + 0.4333333334) equal to 0.674124947 and -0.674124947.


Subproblem 1
x + 0.4333333334 = 0.674124947

Simplifying
x + 0.4333333334 = 0.674124947

Reorder the terms:
0.4333333334 + x = 0.674124947

Solving
0.4333333334 + x = 0.674124947

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x = 0.674124947 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x = 0.674124947 + -0.4333333334
x = 0.674124947 + -0.4333333334

Combine like terms: 0.674124947 + -0.4333333334 = 0.2407916136
x = 0.2407916136

Simplifying
x = 0.2407916136


Subproblem 2
x + 0.4333333334 = -0.674124947

Simplifying
x + 0.4333333334 = -0.674124947

Reorder the terms:
0.4333333334 + x = -0.674124947

Solving
0.4333333334 + x = -0.674124947

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x = -0.674124947 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x = -0.674124947 + -0.4333333334
x = -0.674124947 + -0.4333333334

Combine like terms: -0.674124947 + -0.4333333334 = -1.1074582804
x = -1.1074582804

Simplifying
x = -1.1074582804


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2407916136, -1.1074582804}

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