15x^2+4x-2=0

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


Simplifying
15x2 + 4x + -2 = 0

Reorder the terms:
-2 + 4x + 15x2 = 0

Solving
-2 + 4x + 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'.
-0.1333333333 + 0.2666666667x + x2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + 0.2666666667x + 0.1333333333 + x2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + 0.2666666667x + x2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + 0.2666666667x + x2 = 0 + 0.1333333333
0.2666666667x + x2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
0.2666666667x + x2 = 0.1333333333

The x term is 0.2666666667x.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667x + 0.01777777780 + x2 = 0.1333333333 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667x + x2 = 0.1333333333 + 0.01777777780

Combine like terms: 0.1333333333 + 0.01777777780 = 0.1511111111
0.01777777780 + 0.2666666667x + x2 = 0.1511111111

Factor a perfect square on the left side:
(x + 0.1333333334)(x + 0.1333333334) = 0.1511111111

Calculate the square root of the right side: 0.388730126

Break this problem into two subproblems by setting 
(x + 0.1333333334) equal to 0.388730126 and -0.388730126.


Subproblem 1
x + 0.1333333334 = 0.388730126

Simplifying
x + 0.1333333334 = 0.388730126

Reorder the terms:
0.1333333334 + x = 0.388730126

Solving
0.1333333334 + x = 0.388730126

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = 0.388730126 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = 0.388730126 + -0.1333333334
x = 0.388730126 + -0.1333333334

Combine like terms: 0.388730126 + -0.1333333334 = 0.2553967926
x = 0.2553967926

Simplifying
x = 0.2553967926


Subproblem 2
x + 0.1333333334 = -0.388730126

Simplifying
x + 0.1333333334 = -0.388730126

Reorder the terms:
0.1333333334 + x = -0.388730126

Solving
0.1333333334 + x = -0.388730126

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = -0.388730126 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = -0.388730126 + -0.1333333334
x = -0.388730126 + -0.1333333334

Combine like terms: -0.388730126 + -0.1333333334 = -0.5220634594
x = -0.5220634594

Simplifying
x = -0.5220634594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2553967926, -0.5220634594}

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