23041.79=-705.81x^2+86409x

Solution for 23041.79=-705.81x^2+86409x equation:

Simplifying
23041.79 = -705.81x2 + 86409x

Reorder the terms:
23041.79 = 86409x + -705.81x2

Solving
23041.79 = 86409x + -705.81x2

Solving for variable 'x'.

Reorder the terms:
23041.79 + -86409x + 705.81x2 = 86409x + -86409x + -705.81x2 + 705.81x2

Combine like terms: 86409x + -86409x = 0
23041.79 + -86409x + 705.81x2 = 0 + -705.81x2 + 705.81x2
23041.79 + -86409x + 705.81x2 = -705.81x2 + 705.81x2

Combine like terms: -705.81x2 + 705.81x2 = 0.00
23041.79 + -86409x + 705.81x2 = 0.00

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

Divide each side by '705.81'.
32.64588204 + -122.4252986x + x2 = 0

Move the constant term to the right:

Add '-32.64588204' to each side of the equation.
32.64588204 + -122.4252986x + -32.64588204 + x2 = 0 + -32.64588204

Reorder the terms:
32.64588204 + -32.64588204 + -122.4252986x + x2 = 0 + -32.64588204

Combine like terms: 32.64588204 + -32.64588204 = 0.00000000
0.00000000 + -122.4252986x + x2 = 0 + -32.64588204
-122.4252986x + x2 = 0 + -32.64588204

Combine like terms: 0 + -32.64588204 = -32.64588204
-122.4252986x + x2 = -32.64588204

The x term is -122.4252986x.  Take half its coefficient (-61.2126493).
Square it (3746.988434) and add it to both sides.

Add '3746.988434' to each side of the equation.
-122.4252986x + 3746.988434 + x2 = -32.64588204 + 3746.988434

Reorder the terms:
3746.988434 + -122.4252986x + x2 = -32.64588204 + 3746.988434

Combine like terms: -32.64588204 + 3746.988434 = 3714.34255196
3746.988434 + -122.4252986x + x2 = 3714.34255196

Factor a perfect square on the left side:
(x + -61.2126493)(x + -61.2126493) = 3714.34255196

Calculate the square root of the right side: 60.945406324

Break this problem into two subproblems by setting 
(x + -61.2126493) equal to 60.945406324 and -60.945406324.

Subproblem 1
x + -61.2126493 = 60.945406324

Simplifying
x + -61.2126493 = 60.945406324

Reorder the terms:
-61.2126493 + x = 60.945406324

Solving
-61.2126493 + x = 60.945406324

Solving for variable 'x'.

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

Add '61.2126493' to each side of the equation.
-61.2126493 + 61.2126493 + x = 60.945406324 + 61.2126493

Combine like terms: -61.2126493 + 61.2126493 = 0.0000000
0.0000000 + x = 60.945406324 + 61.2126493
x = 60.945406324 + 61.2126493

Combine like terms: 60.945406324 + 61.2126493 = 122.158055624
x = 122.158055624

Simplifying
x = 122.158055624

Subproblem 2
x + -61.2126493 = -60.945406324

Simplifying
x + -61.2126493 = -60.945406324

Reorder the terms:
-61.2126493 + x = -60.945406324

Solving
-61.2126493 + x = -60.945406324

Solving for variable 'x'.

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

Add '61.2126493' to each side of the equation.
-61.2126493 + 61.2126493 + x = -60.945406324 + 61.2126493

Combine like terms: -61.2126493 + 61.2126493 = 0.0000000
0.0000000 + x = -60.945406324 + 61.2126493
x = -60.945406324 + 61.2126493

Combine like terms: -60.945406324 + 61.2126493 = 0.267242976
x = 0.267242976

Simplifying
x = 0.267242976

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {122.158055624, 0.267242976}