80x^2+1155x-790000=0

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Solution for 80x^2+1155x-790000=0 equation: 


Simplifying
80x2 + 1155x + -790000 = 0

Reorder the terms:
-790000 + 1155x + 80x2 = 0

Solving
-790000 + 1155x + 80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-158000 + 231x + 16x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-158000 + 231x + 16x2)' equal to zero and attempt to solve:

Simplifying
-158000 + 231x + 16x2 = 0

Solving
-158000 + 231x + 16x2 = 0

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

Divide each side by '16'.
-9875 + 14.4375x + x2 = 0

Move the constant term to the right:

Add '9875' to each side of the equation.
-9875 + 14.4375x + 9875 + x2 = 0 + 9875

Reorder the terms:
-9875 + 9875 + 14.4375x + x2 = 0 + 9875

Combine like terms: -9875 + 9875 = 0
0 + 14.4375x + x2 = 0 + 9875
14.4375x + x2 = 0 + 9875

Combine like terms: 0 + 9875 = 9875
14.4375x + x2 = 9875

The x term is 14.4375x.  Take half its coefficient (7.21875).
Square it (52.11035156) and add it to both sides.

Add '52.11035156' to each side of the equation.
14.4375x + 52.11035156 + x2 = 9875 + 52.11035156

Reorder the terms:
52.11035156 + 14.4375x + x2 = 9875 + 52.11035156

Combine like terms: 9875 + 52.11035156 = 9927.11035156
52.11035156 + 14.4375x + x2 = 9927.11035156

Factor a perfect square on the left side:
(x + 7.21875)(x + 7.21875) = 9927.11035156

Calculate the square root of the right side: 99.634885214

Break this problem into two subproblems by setting 
(x + 7.21875) equal to 99.634885214 and -99.634885214.


Subproblem 1
x + 7.21875 = 99.634885214

Simplifying
x + 7.21875 = 99.634885214

Reorder the terms:
7.21875 + x = 99.634885214

Solving
7.21875 + x = 99.634885214

Solving for variable 'x'.

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

Add '-7.21875' to each side of the equation.
7.21875 + -7.21875 + x = 99.634885214 + -7.21875

Combine like terms: 7.21875 + -7.21875 = 0.00000
0.00000 + x = 99.634885214 + -7.21875
x = 99.634885214 + -7.21875

Combine like terms: 99.634885214 + -7.21875 = 92.416135214
x = 92.416135214

Simplifying
x = 92.416135214


Subproblem 2
x + 7.21875 = -99.634885214

Simplifying
x + 7.21875 = -99.634885214

Reorder the terms:
7.21875 + x = -99.634885214

Solving
7.21875 + x = -99.634885214

Solving for variable 'x'.

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

Add '-7.21875' to each side of the equation.
7.21875 + -7.21875 + x = -99.634885214 + -7.21875

Combine like terms: 7.21875 + -7.21875 = 0.00000
0.00000 + x = -99.634885214 + -7.21875
x = -99.634885214 + -7.21875

Combine like terms: -99.634885214 + -7.21875 = -106.853635214
x = -106.853635214

Simplifying
x = -106.853635214


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {92.416135214, -106.853635214}
Solution
x = {92.416135214, -106.853635214}

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