2(x^2-16)+15x=-9x-8

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Solution for 2(x^2-16)+15x=-9x-8 equation: 


Simplifying
2(x2 + -16) + 15x = -9x + -8

Reorder the terms:
2(-16 + x2) + 15x = -9x + -8
(-16 * 2 + x2 * 2) + 15x = -9x + -8
(-32 + 2x2) + 15x = -9x + -8

Reorder the terms:
-32 + 15x + 2x2 = -9x + -8

Reorder the terms:
-32 + 15x + 2x2 = -8 + -9x

Solving
-32 + 15x + 2x2 = -8 + -9x

Solving for variable 'x'.

Reorder the terms:
-32 + 8 + 15x + 9x + 2x2 = -8 + -9x + 8 + 9x

Combine like terms: -32 + 8 = -24
-24 + 15x + 9x + 2x2 = -8 + -9x + 8 + 9x

Combine like terms: 15x + 9x = 24x
-24 + 24x + 2x2 = -8 + -9x + 8 + 9x

Reorder the terms:
-24 + 24x + 2x2 = -8 + 8 + -9x + 9x

Combine like terms: -8 + 8 = 0
-24 + 24x + 2x2 = 0 + -9x + 9x
-24 + 24x + 2x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-24 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 12x + x2 = 0

Solving
-12 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 12x + 12 + x2 = 0 + 12

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

Combine like terms: -12 + 12 = 0
0 + 12x + x2 = 0 + 12
12x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
12x + x2 = 12

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 12 + 36

Reorder the terms:
36 + 12x + x2 = 12 + 36

Combine like terms: 12 + 36 = 48
36 + 12x + x2 = 48

Factor a perfect square on the left side:
(x + 6)(x + 6) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 6) equal to 6.92820323 and -6.92820323.


Subproblem 1
x + 6 = 6.92820323

Simplifying
x + 6 = 6.92820323

Reorder the terms:
6 + x = 6.92820323

Solving
6 + x = 6.92820323

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 6.92820323 + -6

Combine like terms: 6 + -6 = 0
0 + x = 6.92820323 + -6
x = 6.92820323 + -6

Combine like terms: 6.92820323 + -6 = 0.92820323
x = 0.92820323

Simplifying
x = 0.92820323


Subproblem 2
x + 6 = -6.92820323

Simplifying
x + 6 = -6.92820323

Reorder the terms:
6 + x = -6.92820323

Solving
6 + x = -6.92820323

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -6.92820323 + -6

Combine like terms: 6 + -6 = 0
0 + x = -6.92820323 + -6
x = -6.92820323 + -6

Combine like terms: -6.92820323 + -6 = -12.92820323
x = -12.92820323

Simplifying
x = -12.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.92820323, -12.92820323}
Solution
x = {0.92820323, -12.92820323}

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