x^2+52x-676=0

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Solution for x^2+52x-676=0 equation: 


Simplifying
x2 + 52x + -676 = 0

Reorder the terms:
-676 + 52x + x2 = 0

Solving
-676 + 52x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '676' to each side of the equation.
-676 + 52x + 676 + x2 = 0 + 676

Reorder the terms:
-676 + 676 + 52x + x2 = 0 + 676

Combine like terms: -676 + 676 = 0
0 + 52x + x2 = 0 + 676
52x + x2 = 0 + 676

Combine like terms: 0 + 676 = 676
52x + x2 = 676

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 = 676 + 676

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

Combine like terms: 676 + 676 = 1352
676 + 52x + x2 = 1352

Factor a perfect square on the left side:
(x + 26)(x + 26) = 1352

Calculate the square root of the right side: 36.769552622

Break this problem into two subproblems by setting 
(x + 26) equal to 36.769552622 and -36.769552622.


Subproblem 1
x + 26 = 36.769552622

Simplifying
x + 26 = 36.769552622

Reorder the terms:
26 + x = 36.769552622

Solving
26 + x = 36.769552622

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 = 36.769552622 + -26

Combine like terms: 26 + -26 = 0
0 + x = 36.769552622 + -26
x = 36.769552622 + -26

Combine like terms: 36.769552622 + -26 = 10.769552622
x = 10.769552622

Simplifying
x = 10.769552622


Subproblem 2
x + 26 = -36.769552622

Simplifying
x + 26 = -36.769552622

Reorder the terms:
26 + x = -36.769552622

Solving
26 + x = -36.769552622

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 = -36.769552622 + -26

Combine like terms: 26 + -26 = 0
0 + x = -36.769552622 + -26
x = -36.769552622 + -26

Combine like terms: -36.769552622 + -26 = -62.769552622
x = -62.769552622

Simplifying
x = -62.769552622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.769552622, -62.769552622}

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