15x^2+22x-12=0

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Solution for 15x^2+22x-12=0 equation: 


Simplifying
15x2 + 22x + -12 = 0

Reorder the terms:
-12 + 22x + 15x2 = 0

Solving
-12 + 22x + 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'.
-0.8 + 1.466666667x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 1.466666667x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 1.466666667x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 1.466666667x + x2 = 0 + 0.8
1.466666667x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
1.466666667x + x2 = 0.8

The x term is 1.466666667x.  Take half its coefficient (0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
1.466666667x + 0.5377777780 + x2 = 0.8 + 0.5377777780

Reorder the terms:
0.5377777780 + 1.466666667x + x2 = 0.8 + 0.5377777780

Combine like terms: 0.8 + 0.5377777780 = 1.337777778
0.5377777780 + 1.466666667x + x2 = 1.337777778

Factor a perfect square on the left side:
(x + 0.7333333335)(x + 0.7333333335) = 1.337777778

Calculate the square root of the right side: 1.156623438

Break this problem into two subproblems by setting 
(x + 0.7333333335) equal to 1.156623438 and -1.156623438.


Subproblem 1
x + 0.7333333335 = 1.156623438

Simplifying
x + 0.7333333335 = 1.156623438

Reorder the terms:
0.7333333335 + x = 1.156623438

Solving
0.7333333335 + x = 1.156623438

Solving for variable 'x'.

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

Add '-0.7333333335' to each side of the equation.
0.7333333335 + -0.7333333335 + x = 1.156623438 + -0.7333333335

Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000
0.0000000000 + x = 1.156623438 + -0.7333333335
x = 1.156623438 + -0.7333333335

Combine like terms: 1.156623438 + -0.7333333335 = 0.4232901045
x = 0.4232901045

Simplifying
x = 0.4232901045


Subproblem 2
x + 0.7333333335 = -1.156623438

Simplifying
x + 0.7333333335 = -1.156623438

Reorder the terms:
0.7333333335 + x = -1.156623438

Solving
0.7333333335 + x = -1.156623438

Solving for variable 'x'.

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

Add '-0.7333333335' to each side of the equation.
0.7333333335 + -0.7333333335 + x = -1.156623438 + -0.7333333335

Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000
0.0000000000 + x = -1.156623438 + -0.7333333335
x = -1.156623438 + -0.7333333335

Combine like terms: -1.156623438 + -0.7333333335 = -1.8899567715
x = -1.8899567715

Simplifying
x = -1.8899567715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4232901045, -1.8899567715}

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