23x^2=3344-x

Solution for 23x^2=3344-x equation:

Simplifying
23x2 = 3344 + -1x

Solving
23x2 = 3344 + -1x

Solving for variable 'x'.

Reorder the terms:
-3344 + x + 23x2 = 3344 + -1x + -3344 + x

Reorder the terms:
-3344 + x + 23x2 = 3344 + -3344 + -1x + x

Combine like terms: 3344 + -3344 = 0
-3344 + x + 23x2 = 0 + -1x + x
-3344 + x + 23x2 = -1x + x

Combine like terms: -1x + x = 0
-3344 + x + 23x2 = 0

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

Divide each side by '23'.
-145.3913043 + 0.04347826087x + x2 = 0

Move the constant term to the right:

Add '145.3913043' to each side of the equation.
-145.3913043 + 0.04347826087x + 145.3913043 + x2 = 0 + 145.3913043

Reorder the terms:
-145.3913043 + 145.3913043 + 0.04347826087x + x2 = 0 + 145.3913043

Combine like terms: -145.3913043 + 145.3913043 = 0.0000000
0.0000000 + 0.04347826087x + x2 = 0 + 145.3913043
0.04347826087x + x2 = 0 + 145.3913043

Combine like terms: 0 + 145.3913043 = 145.3913043
0.04347826087x + x2 = 145.3913043

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.04347826087x + 0.25 + x2 = 145.3913043 + 0.25

Reorder the terms:
0.25 + 0.04347826087x + x2 = 145.3913043 + 0.25

Combine like terms: 145.3913043 + 0.25 = 145.6413043
0.25 + 0.04347826087x + x2 = 145.6413043

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 145.6413043

Calculate the square root of the right side: 12.068193912

Break this problem into two subproblems by setting 
(x + 0.5) equal to 12.068193912 and -12.068193912.

Subproblem 1
x + 0.5 = 12.068193912

Simplifying
x + 0.5 = 12.068193912

Reorder the terms:
0.5 + x = 12.068193912

Solving
0.5 + x = 12.068193912

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 12.068193912 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 12.068193912 + -0.5
x = 12.068193912 + -0.5

Combine like terms: 12.068193912 + -0.5 = 11.568193912
x = 11.568193912

Simplifying
x = 11.568193912

Subproblem 2
x + 0.5 = -12.068193912

Simplifying
x + 0.5 = -12.068193912

Reorder the terms:
0.5 + x = -12.068193912

Solving
0.5 + x = -12.068193912

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -12.068193912 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -12.068193912 + -0.5
x = -12.068193912 + -0.5

Combine like terms: -12.068193912 + -0.5 = -12.568193912
x = -12.568193912

Simplifying
x = -12.568193912

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.568193912, -12.568193912}