-8x^2-90x+80=0

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Solution for -8x^2-90x+80=0 equation: 


Simplifying
-8x2 + -90x + 80 = 0

Reorder the terms:
80 + -90x + -8x2 = 0

Solving
80 + -90x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -45x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -45x + -4x2)' equal to zero and attempt to solve:

Simplifying
40 + -45x + -4x2 = 0

Solving
40 + -45x + -4x2 = 0

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

Divide each side by '-4'.
-10 + 11.25x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 11.25x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 11.25x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 11.25x + x2 = 0 + 10
11.25x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
11.25x + x2 = 10

The x term is 11.25x.  Take half its coefficient (5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
11.25x + 31.640625 + x2 = 10 + 31.640625

Reorder the terms:
31.640625 + 11.25x + x2 = 10 + 31.640625

Combine like terms: 10 + 31.640625 = 41.640625
31.640625 + 11.25x + x2 = 41.640625

Factor a perfect square on the left side:
(x + 5.625)(x + 5.625) = 41.640625

Calculate the square root of the right side: 6.45295475

Break this problem into two subproblems by setting 
(x + 5.625) equal to 6.45295475 and -6.45295475.


Subproblem 1
x + 5.625 = 6.45295475

Simplifying
x + 5.625 = 6.45295475

Reorder the terms:
5.625 + x = 6.45295475

Solving
5.625 + x = 6.45295475

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = 6.45295475 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = 6.45295475 + -5.625
x = 6.45295475 + -5.625

Combine like terms: 6.45295475 + -5.625 = 0.82795475
x = 0.82795475

Simplifying
x = 0.82795475


Subproblem 2
x + 5.625 = -6.45295475

Simplifying
x + 5.625 = -6.45295475

Reorder the terms:
5.625 + x = -6.45295475

Solving
5.625 + x = -6.45295475

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = -6.45295475 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = -6.45295475 + -5.625
x = -6.45295475 + -5.625

Combine like terms: -6.45295475 + -5.625 = -12.07795475
x = -12.07795475

Simplifying
x = -12.07795475


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.82795475, -12.07795475}
Solution
x = {0.82795475, -12.07795475}

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