-16x^2-20x+140=0

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Solution for -16x^2-20x+140=0 equation: 


Simplifying
-16x2 + -20x + 140 = 0

Reorder the terms:
140 + -20x + -16x2 = 0

Solving
140 + -20x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -5x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(35 + -5x + -4x2)' equal to zero and attempt to solve:

Simplifying
35 + -5x + -4x2 = 0

Solving
35 + -5x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-8.75 + 1.25x + x2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 1.25x + 8.75 + x2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + 1.25x + x2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 1.25x + x2 = 0 + 8.75
1.25x + x2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
1.25x + x2 = 8.75

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 = 8.75 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 8.75 + 0.390625

Combine like terms: 8.75 + 0.390625 = 9.140625
0.390625 + 1.25x + x2 = 9.140625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 9.140625

Calculate the square root of the right side: 3.023346656

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.023346656 and -3.023346656.


Subproblem 1
x + 0.625 = 3.023346656

Simplifying
x + 0.625 = 3.023346656

Reorder the terms:
0.625 + x = 3.023346656

Solving
0.625 + x = 3.023346656

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 = 3.023346656 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 3.023346656 + -0.625
x = 3.023346656 + -0.625

Combine like terms: 3.023346656 + -0.625 = 2.398346656
x = 2.398346656

Simplifying
x = 2.398346656


Subproblem 2
x + 0.625 = -3.023346656

Simplifying
x + 0.625 = -3.023346656

Reorder the terms:
0.625 + x = -3.023346656

Solving
0.625 + x = -3.023346656

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 = -3.023346656 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -3.023346656 + -0.625
x = -3.023346656 + -0.625

Combine like terms: -3.023346656 + -0.625 = -3.648346656
x = -3.648346656

Simplifying
x = -3.648346656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.398346656, -3.648346656}
Solution
x = {2.398346656, -3.648346656}

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