15x^2+8x-36=0

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Solution for 15x^2+8x-36=0 equation: 


Simplifying
15x2 + 8x + -36 = 0

Reorder the terms:
-36 + 8x + 15x2 = 0

Solving
-36 + 8x + 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'.
-2.4 + 0.5333333333x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.5333333333x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.5333333333x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.5333333333x + x2 = 0 + 2.4
0.5333333333x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.5333333333x + x2 = 2.4

The x term is 0.5333333333x.  Take half its coefficient (0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
0.5333333333x + 0.07111111113 + x2 = 2.4 + 0.07111111113

Reorder the terms:
0.07111111113 + 0.5333333333x + x2 = 2.4 + 0.07111111113

Combine like terms: 2.4 + 0.07111111113 = 2.47111111113
0.07111111113 + 0.5333333333x + x2 = 2.47111111113

Factor a perfect square on the left side:
(x + 0.2666666667)(x + 0.2666666667) = 2.47111111113

Calculate the square root of the right side: 1.571976816

Break this problem into two subproblems by setting 
(x + 0.2666666667) equal to 1.571976816 and -1.571976816.


Subproblem 1
x + 0.2666666667 = 1.571976816

Simplifying
x + 0.2666666667 = 1.571976816

Reorder the terms:
0.2666666667 + x = 1.571976816

Solving
0.2666666667 + x = 1.571976816

Solving for variable 'x'.

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

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -0.2666666667 + x = 1.571976816 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + x = 1.571976816 + -0.2666666667
x = 1.571976816 + -0.2666666667

Combine like terms: 1.571976816 + -0.2666666667 = 1.3053101493
x = 1.3053101493

Simplifying
x = 1.3053101493


Subproblem 2
x + 0.2666666667 = -1.571976816

Simplifying
x + 0.2666666667 = -1.571976816

Reorder the terms:
0.2666666667 + x = -1.571976816

Solving
0.2666666667 + x = -1.571976816

Solving for variable 'x'.

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

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -0.2666666667 + x = -1.571976816 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + x = -1.571976816 + -0.2666666667
x = -1.571976816 + -0.2666666667

Combine like terms: -1.571976816 + -0.2666666667 = -1.8386434827
x = -1.8386434827

Simplifying
x = -1.8386434827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3053101493, -1.8386434827}

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