15x^2-10x-8=0

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Solution for 15x^2-10x-8=0 equation: 


Simplifying
15x2 + -10x + -8 = 0

Reorder the terms:
-8 + -10x + 15x2 = 0

Solving
-8 + -10x + 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'.
-0.5333333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.5333333333' to each side of the equation.
-0.5333333333 + -0.6666666667x + 0.5333333333 + x2 = 0 + 0.5333333333

Reorder the terms:
-0.5333333333 + 0.5333333333 + -0.6666666667x + x2 = 0 + 0.5333333333

Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + 0.5333333333
-0.6666666667x + x2 = 0 + 0.5333333333

Combine like terms: 0 + 0.5333333333 = 0.5333333333
-0.6666666667x + x2 = 0.5333333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 0.5333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 0.5333333333 + 0.1111111112

Combine like terms: 0.5333333333 + 0.1111111112 = 0.6444444445
0.1111111112 + -0.6666666667x + x2 = 0.6444444445

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.6444444445

Calculate the square root of the right side: 0.802772972

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.802772972 and -0.802772972.


Subproblem 1
x + -0.3333333334 = 0.802772972

Simplifying
x + -0.3333333334 = 0.802772972

Reorder the terms:
-0.3333333334 + x = 0.802772972

Solving
-0.3333333334 + x = 0.802772972

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 0.802772972 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 0.802772972 + 0.3333333334
x = 0.802772972 + 0.3333333334

Combine like terms: 0.802772972 + 0.3333333334 = 1.1361063054
x = 1.1361063054

Simplifying
x = 1.1361063054


Subproblem 2
x + -0.3333333334 = -0.802772972

Simplifying
x + -0.3333333334 = -0.802772972

Reorder the terms:
-0.3333333334 + x = -0.802772972

Solving
-0.3333333334 + x = -0.802772972

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -0.802772972 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -0.802772972 + 0.3333333334
x = -0.802772972 + 0.3333333334

Combine like terms: -0.802772972 + 0.3333333334 = -0.4694396386
x = -0.4694396386

Simplifying
x = -0.4694396386


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1361063054, -0.4694396386}

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