15x^2-5-12x=0

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Solution for 15x^2-5-12x=0 equation: 


Simplifying
15x2 + -5 + -12x = 0

Reorder the terms:
-5 + -12x + 15x2 = 0

Solving
-5 + -12x + 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'.
-0.3333333333 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.8x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.8x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.8x + x2 = 0 + 0.3333333333
-0.8x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.8x + x2 = 0.3333333333

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.3333333333 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.3333333333 + 0.16

Combine like terms: 0.3333333333 + 0.16 = 0.4933333333
0.16 + -0.8x + x2 = 0.4933333333

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.4933333333

Calculate the square root of the right side: 0.702376917

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.702376917 and -0.702376917.


Subproblem 1
x + -0.4 = 0.702376917

Simplifying
x + -0.4 = 0.702376917

Reorder the terms:
-0.4 + x = 0.702376917

Solving
-0.4 + x = 0.702376917

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.702376917 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.702376917 + 0.4
x = 0.702376917 + 0.4

Combine like terms: 0.702376917 + 0.4 = 1.102376917
x = 1.102376917

Simplifying
x = 1.102376917


Subproblem 2
x + -0.4 = -0.702376917

Simplifying
x + -0.4 = -0.702376917

Reorder the terms:
-0.4 + x = -0.702376917

Solving
-0.4 + x = -0.702376917

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.702376917 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.702376917 + 0.4
x = -0.702376917 + 0.4

Combine like terms: -0.702376917 + 0.4 = -0.302376917
x = -0.302376917

Simplifying
x = -0.302376917


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.102376917, -0.302376917}

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