158000x^2-258x-80=0

Solution for 158000x^2-258x-80=0 equation:

Simplifying
158000x2 + -258x + -80 = 0

Reorder the terms:
-80 + -258x + 158000x2 = 0

Solving
-80 + -258x + 158000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -129x + 79000x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-40 + -129x + 79000x2)' equal to zero and attempt to solve:

Simplifying
-40 + -129x + 79000x2 = 0

Solving
-40 + -129x + 79000x2 = 0

Begin completing the square.  Divide all terms by
79000 the coefficient of the squared term: 

Divide each side by '79000'.
-0.0005063291139 + -0.001632911392x + x2 = 0.000

Move the constant term to the right:

Add '0.0005063291139' to each side of the equation.
-0.0005063291139 + -0.001632911392x + 0.0005063291139 + x2 = 0.000 + 0.0005063291139

Reorder the terms:
-0.0005063291139 + 0.0005063291139 + -0.001632911392x + x2 = 0.000 + 0.0005063291139

Combine like terms: -0.0005063291139 + 0.0005063291139 = 0.0000000000000
0.0000000000000 + -0.001632911392x + x2 = 0.000 + 0.0005063291139
-0.001632911392x + x2 = 0.000 + 0.0005063291139

Combine like terms: 0.000 + 0.0005063291139 = 0.0005063291139
-0.001632911392x + x2 = 0.0005063291139

The x term is -0.001632911392x.  Take half its coefficient (-0.000816455696).
Square it (0.0000006665999035) and add it to both sides.

Add '0.0000006665999035' to each side of the equation.
-0.001632911392x + 0.0000006665999035 + x2 = 0.0005063291139 + 0.0000006665999035

Reorder the terms:
0.0000006665999035 + -0.001632911392x + x2 = 0.0005063291139 + 0.0000006665999035

Combine like terms: 0.0005063291139 + 0.0000006665999035 = 0.0005069957138035
0.0000006665999035 + -0.001632911392x + x2 = 0.0005069957138035

Factor a perfect square on the left side:
(x + -0.000816455696)(x + -0.000816455696) = 0.0005069957138035

Calculate the square root of the right side: 0.022516565

Break this problem into two subproblems by setting 
(x + -0.000816455696) equal to 0.022516565 and -0.022516565.

Subproblem 1
x + -0.000816455696 = 0.022516565

Simplifying
x + -0.000816455696 = 0.022516565

Reorder the terms:
-0.000816455696 + x = 0.022516565

Solving
-0.000816455696 + x = 0.022516565

Solving for variable 'x'.

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

Add '0.000816455696' to each side of the equation.
-0.000816455696 + 0.000816455696 + x = 0.022516565 + 0.000816455696

Combine like terms: -0.000816455696 + 0.000816455696 = 0.000000000000
0.000000000000 + x = 0.022516565 + 0.000816455696
x = 0.022516565 + 0.000816455696

Combine like terms: 0.022516565 + 0.000816455696 = 0.023333020696
x = 0.023333020696

Simplifying
x = 0.023333020696

Subproblem 2
x + -0.000816455696 = -0.022516565

Simplifying
x + -0.000816455696 = -0.022516565

Reorder the terms:
-0.000816455696 + x = -0.022516565

Solving
-0.000816455696 + x = -0.022516565

Solving for variable 'x'.

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

Add '0.000816455696' to each side of the equation.
-0.000816455696 + 0.000816455696 + x = -0.022516565 + 0.000816455696

Combine like terms: -0.000816455696 + 0.000816455696 = 0.000000000000
0.000000000000 + x = -0.022516565 + 0.000816455696
x = -0.022516565 + 0.000816455696

Combine like terms: -0.022516565 + 0.000816455696 = -0.021700109304
x = -0.021700109304

Simplifying
x = -0.021700109304

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.023333020696, -0.021700109304}
Solution
x = {0.023333020696, -0.021700109304}