-16x^2-20x+180=50

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Solution for -16x^2-20x+180=50 equation: 


Simplifying
-16x2 + -20x + 180 = 50

Reorder the terms:
180 + -20x + -16x2 = 50

Solving
180 + -20x + -16x2 = 50

Solving for variable 'x'.

Reorder the terms:
180 + -50 + -20x + -16x2 = 50 + -50

Combine like terms: 180 + -50 = 130
130 + -20x + -16x2 = 50 + -50

Combine like terms: 50 + -50 = 0
130 + -20x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + -10x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(65 + -10x + -8x2)' equal to zero and attempt to solve:

Simplifying
65 + -10x + -8x2 = 0

Solving
65 + -10x + -8x2 = 0

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

Divide each side by '-8'.
-8.125 + 1.25x + x2 = 0

Move the constant term to the right:

Add '8.125' to each side of the equation.
-8.125 + 1.25x + 8.125 + x2 = 0 + 8.125

Reorder the terms:
-8.125 + 8.125 + 1.25x + x2 = 0 + 8.125

Combine like terms: -8.125 + 8.125 = 0.000
0.000 + 1.25x + x2 = 0 + 8.125
1.25x + x2 = 0 + 8.125

Combine like terms: 0 + 8.125 = 8.125
1.25x + x2 = 8.125

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 8.125 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 8.125 + 0.390625

Combine like terms: 8.125 + 0.390625 = 8.515625
0.390625 + 1.25x + x2 = 8.515625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 8.515625

Calculate the square root of the right side: 2.918154382

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.918154382 and -2.918154382.


Subproblem 1
x + 0.625 = 2.918154382

Simplifying
x + 0.625 = 2.918154382

Reorder the terms:
0.625 + x = 2.918154382

Solving
0.625 + x = 2.918154382

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 2.918154382 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.918154382 + -0.625
x = 2.918154382 + -0.625

Combine like terms: 2.918154382 + -0.625 = 2.293154382
x = 2.293154382

Simplifying
x = 2.293154382


Subproblem 2
x + 0.625 = -2.918154382

Simplifying
x + 0.625 = -2.918154382

Reorder the terms:
0.625 + x = -2.918154382

Solving
0.625 + x = -2.918154382

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -2.918154382 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.918154382 + -0.625
x = -2.918154382 + -0.625

Combine like terms: -2.918154382 + -0.625 = -3.543154382
x = -3.543154382

Simplifying
x = -3.543154382


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.293154382, -3.543154382}
Solution
x = {2.293154382, -3.543154382}

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