x^2-12.26x=336

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Solution for x^2-12.26x=336 equation: 


Simplifying
x2 + -12.26x = 336

Reorder the terms:
-12.26x + x2 = 336

Solving
-12.26x + x2 = 336

Solving for variable 'x'.

Reorder the terms:
-336 + -12.26x + x2 = 336 + -336

Combine like terms: 336 + -336 = 0
-336 + -12.26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '336' to each side of the equation.
-336 + -12.26x + 336 + x2 = 0 + 336

Reorder the terms:
-336 + 336 + -12.26x + x2 = 0 + 336

Combine like terms: -336 + 336 = 0
0 + -12.26x + x2 = 0 + 336
-12.26x + x2 = 0 + 336

Combine like terms: 0 + 336 = 336
-12.26x + x2 = 336

The x term is -12.26x.  Take half its coefficient (-6.13).
Square it (37.5769) and add it to both sides.

Add '37.5769' to each side of the equation.
-12.26x + 37.5769 + x2 = 336 + 37.5769

Reorder the terms:
37.5769 + -12.26x + x2 = 336 + 37.5769

Combine like terms: 336 + 37.5769 = 373.5769
37.5769 + -12.26x + x2 = 373.5769

Factor a perfect square on the left side:
(x + -6.13)(x + -6.13) = 373.5769

Calculate the square root of the right side: 19.32813752

Break this problem into two subproblems by setting 
(x + -6.13) equal to 19.32813752 and -19.32813752.


Subproblem 1
x + -6.13 = 19.32813752

Simplifying
x + -6.13 = 19.32813752

Reorder the terms:
-6.13 + x = 19.32813752

Solving
-6.13 + x = 19.32813752

Solving for variable 'x'.

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

Add '6.13' to each side of the equation.
-6.13 + 6.13 + x = 19.32813752 + 6.13

Combine like terms: -6.13 + 6.13 = 0.00
0.00 + x = 19.32813752 + 6.13
x = 19.32813752 + 6.13

Combine like terms: 19.32813752 + 6.13 = 25.45813752
x = 25.45813752

Simplifying
x = 25.45813752


Subproblem 2
x + -6.13 = -19.32813752

Simplifying
x + -6.13 = -19.32813752

Reorder the terms:
-6.13 + x = -19.32813752

Solving
-6.13 + x = -19.32813752

Solving for variable 'x'.

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

Add '6.13' to each side of the equation.
-6.13 + 6.13 + x = -19.32813752 + 6.13

Combine like terms: -6.13 + 6.13 = 0.00
0.00 + x = -19.32813752 + 6.13
x = -19.32813752 + 6.13

Combine like terms: -19.32813752 + 6.13 = -13.19813752
x = -13.19813752

Simplifying
x = -13.19813752


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.45813752, -13.19813752}

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