-0.1417x^2+23.365x=946.12

Solution for -0.1417x^2+23.365x=946.12 equation:

Simplifying
-0.1417x2 + 23.365x = 946.12

Reorder the terms:
23.365x + -0.1417x2 = 946.12

Solving
23.365x + -0.1417x2 = 946.12

Solving for variable 'x'.

Reorder the terms:
-946.12 + 23.365x + -0.1417x2 = 946.12 + -946.12

Combine like terms: 946.12 + -946.12 = 0.00
-946.12 + 23.365x + -0.1417x2 = 0.00

Begin completing the square.  Divide all terms by
-0.1417 the coefficient of the squared term: 

Divide each side by '-0.1417'.
6676.923077 + -164.890614x + x2 = 0

Move the constant term to the right:

Add '-6676.923077' to each side of the equation.
6676.923077 + -164.890614x + -6676.923077 + x2 = 0 + -6676.923077

Reorder the terms:
6676.923077 + -6676.923077 + -164.890614x + x2 = 0 + -6676.923077

Combine like terms: 6676.923077 + -6676.923077 = 0.000000
0.000000 + -164.890614x + x2 = 0 + -6676.923077
-164.890614x + x2 = 0 + -6676.923077

Combine like terms: 0 + -6676.923077 = -6676.923077
-164.890614x + x2 = -6676.923077

The x term is -164.890614x.  Take half its coefficient (-82.445307).
Square it (6797.228646) and add it to both sides.

Add '6797.228646' to each side of the equation.
-164.890614x + 6797.228646 + x2 = -6676.923077 + 6797.228646

Reorder the terms:
6797.228646 + -164.890614x + x2 = -6676.923077 + 6797.228646

Combine like terms: -6676.923077 + 6797.228646 = 120.305569
6797.228646 + -164.890614x + x2 = 120.305569

Factor a perfect square on the left side:
(x + -82.445307)(x + -82.445307) = 120.305569

Calculate the square root of the right side: 10.968389535

Break this problem into two subproblems by setting 
(x + -82.445307) equal to 10.968389535 and -10.968389535.

Subproblem 1
x + -82.445307 = 10.968389535

Simplifying
x + -82.445307 = 10.968389535

Reorder the terms:
-82.445307 + x = 10.968389535

Solving
-82.445307 + x = 10.968389535

Solving for variable 'x'.

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

Add '82.445307' to each side of the equation.
-82.445307 + 82.445307 + x = 10.968389535 + 82.445307

Combine like terms: -82.445307 + 82.445307 = 0.000000
0.000000 + x = 10.968389535 + 82.445307
x = 10.968389535 + 82.445307

Combine like terms: 10.968389535 + 82.445307 = 93.413696535
x = 93.413696535

Simplifying
x = 93.413696535

Subproblem 2
x + -82.445307 = -10.968389535

Simplifying
x + -82.445307 = -10.968389535

Reorder the terms:
-82.445307 + x = -10.968389535

Solving
-82.445307 + x = -10.968389535

Solving for variable 'x'.

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

Add '82.445307' to each side of the equation.
-82.445307 + 82.445307 + x = -10.968389535 + 82.445307

Combine like terms: -82.445307 + 82.445307 = 0.000000
0.000000 + x = -10.968389535 + 82.445307
x = -10.968389535 + 82.445307

Combine like terms: -10.968389535 + 82.445307 = 71.476917465
x = 71.476917465

Simplifying
x = 71.476917465

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {93.413696535, 71.476917465}