15x^2-64x-480=0

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Solution for 15x^2-64x-480=0 equation: 


Simplifying
15x2 + -64x + -480 = 0

Reorder the terms:
-480 + -64x + 15x2 = 0

Solving
-480 + -64x + 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'.
-32 + -4.266666667x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -4.266666667x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -4.266666667x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -4.266666667x + x2 = 0 + 32
-4.266666667x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-4.266666667x + x2 = 32

The x term is -4.266666667x.  Take half its coefficient (-2.133333334).
Square it (4.551111114) and add it to both sides.

Add '4.551111114' to each side of the equation.
-4.266666667x + 4.551111114 + x2 = 32 + 4.551111114

Reorder the terms:
4.551111114 + -4.266666667x + x2 = 32 + 4.551111114

Combine like terms: 32 + 4.551111114 = 36.551111114
4.551111114 + -4.266666667x + x2 = 36.551111114

Factor a perfect square on the left side:
(x + -2.133333334)(x + -2.133333334) = 36.551111114

Calculate the square root of the right side: 6.045751493

Break this problem into two subproblems by setting 
(x + -2.133333334) equal to 6.045751493 and -6.045751493.


Subproblem 1
x + -2.133333334 = 6.045751493

Simplifying
x + -2.133333334 = 6.045751493

Reorder the terms:
-2.133333334 + x = 6.045751493

Solving
-2.133333334 + x = 6.045751493

Solving for variable 'x'.

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

Add '2.133333334' to each side of the equation.
-2.133333334 + 2.133333334 + x = 6.045751493 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = 6.045751493 + 2.133333334
x = 6.045751493 + 2.133333334

Combine like terms: 6.045751493 + 2.133333334 = 8.179084827
x = 8.179084827

Simplifying
x = 8.179084827


Subproblem 2
x + -2.133333334 = -6.045751493

Simplifying
x + -2.133333334 = -6.045751493

Reorder the terms:
-2.133333334 + x = -6.045751493

Solving
-2.133333334 + x = -6.045751493

Solving for variable 'x'.

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

Add '2.133333334' to each side of the equation.
-2.133333334 + 2.133333334 + x = -6.045751493 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = -6.045751493 + 2.133333334
x = -6.045751493 + 2.133333334

Combine like terms: -6.045751493 + 2.133333334 = -3.912418159
x = -3.912418159

Simplifying
x = -3.912418159


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.179084827, -3.912418159}

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