x^2-52x+336=0

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Solution for x^2-52x+336=0 equation: 


Simplifying
x2 + -52x + 336 = 0

Reorder the terms:
336 + -52x + x2 = 0

Solving
336 + -52x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-336' to each side of the equation.
336 + -52x + -336 + x2 = 0 + -336

Reorder the terms:
336 + -336 + -52x + x2 = 0 + -336

Combine like terms: 336 + -336 = 0
0 + -52x + x2 = 0 + -336
-52x + x2 = 0 + -336

Combine like terms: 0 + -336 = -336
-52x + x2 = -336

The x term is -52x.  Take half its coefficient (-26).
Square it (676) and add it to both sides.

Add '676' to each side of the equation.
-52x + 676 + x2 = -336 + 676

Reorder the terms:
676 + -52x + x2 = -336 + 676

Combine like terms: -336 + 676 = 340
676 + -52x + x2 = 340

Factor a perfect square on the left side:
(x + -26)(x + -26) = 340

Calculate the square root of the right side: 18.439088915

Break this problem into two subproblems by setting 
(x + -26) equal to 18.439088915 and -18.439088915.


Subproblem 1
x + -26 = 18.439088915

Simplifying
x + -26 = 18.439088915

Reorder the terms:
-26 + x = 18.439088915

Solving
-26 + x = 18.439088915

Solving for variable 'x'.

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

Add '26' to each side of the equation.
-26 + 26 + x = 18.439088915 + 26

Combine like terms: -26 + 26 = 0
0 + x = 18.439088915 + 26
x = 18.439088915 + 26

Combine like terms: 18.439088915 + 26 = 44.439088915
x = 44.439088915

Simplifying
x = 44.439088915


Subproblem 2
x + -26 = -18.439088915

Simplifying
x + -26 = -18.439088915

Reorder the terms:
-26 + x = -18.439088915

Solving
-26 + x = -18.439088915

Solving for variable 'x'.

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

Add '26' to each side of the equation.
-26 + 26 + x = -18.439088915 + 26

Combine like terms: -26 + 26 = 0
0 + x = -18.439088915 + 26
x = -18.439088915 + 26

Combine like terms: -18.439088915 + 26 = 7.560911085
x = 7.560911085

Simplifying
x = 7.560911085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.439088915, 7.560911085}

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