2=-16x^2-120x

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Solution for 2=-16x^2-120x equation: 


Simplifying
2 = -16x2 + -120x

Reorder the terms:
2 = -120x + -16x2

Solving
2 = -120x + -16x2

Solving for variable 'x'.

Reorder the terms:
2 + 120x + 16x2 = -120x + 120x + -16x2 + 16x2

Combine like terms: -120x + 120x = 0
2 + 120x + 16x2 = 0 + -16x2 + 16x2
2 + 120x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
2 + 120x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 60x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 60x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 60x + 8x2 = 0

Solving
1 + 60x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 7.5x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 7.5x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 7.5x + x2 = 0 + -0.125
7.5x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
7.5x + x2 = -0.125

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -0.125 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -0.125 + 14.0625

Combine like terms: -0.125 + 14.0625 = 13.9375
14.0625 + 7.5x + x2 = 13.9375

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 13.9375

Calculate the square root of the right side: 3.733296131

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.733296131 and -3.733296131.


Subproblem 1
x + 3.75 = 3.733296131

Simplifying
x + 3.75 = 3.733296131

Reorder the terms:
3.75 + x = 3.733296131

Solving
3.75 + x = 3.733296131

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.733296131 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.733296131 + -3.75
x = 3.733296131 + -3.75

Combine like terms: 3.733296131 + -3.75 = -0.016703869
x = -0.016703869

Simplifying
x = -0.016703869


Subproblem 2
x + 3.75 = -3.733296131

Simplifying
x + 3.75 = -3.733296131

Reorder the terms:
3.75 + x = -3.733296131

Solving
3.75 + x = -3.733296131

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.733296131 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.733296131 + -3.75
x = -3.733296131 + -3.75

Combine like terms: -3.733296131 + -3.75 = -7.483296131
x = -7.483296131

Simplifying
x = -7.483296131


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.016703869, -7.483296131}
Solution
x = {-0.016703869, -7.483296131}

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