x^2-52x-7=0

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Solution for x^2-52x-7=0 equation: 


Simplifying
x2 + -52x + -7 = 0

Reorder the terms:
-7 + -52x + x2 = 0

Solving
-7 + -52x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -52x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -52x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -52x + x2 = 0 + 7
-52x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-52x + x2 = 7

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 = 7 + 676

Reorder the terms:
676 + -52x + x2 = 7 + 676

Combine like terms: 7 + 676 = 683
676 + -52x + x2 = 683

Factor a perfect square on the left side:
(x + -26)(x + -26) = 683

Calculate the square root of the right side: 26.134268691

Break this problem into two subproblems by setting 
(x + -26) equal to 26.134268691 and -26.134268691.


Subproblem 1
x + -26 = 26.134268691

Simplifying
x + -26 = 26.134268691

Reorder the terms:
-26 + x = 26.134268691

Solving
-26 + x = 26.134268691

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 = 26.134268691 + 26

Combine like terms: -26 + 26 = 0
0 + x = 26.134268691 + 26
x = 26.134268691 + 26

Combine like terms: 26.134268691 + 26 = 52.134268691
x = 52.134268691

Simplifying
x = 52.134268691


Subproblem 2
x + -26 = -26.134268691

Simplifying
x + -26 = -26.134268691

Reorder the terms:
-26 + x = -26.134268691

Solving
-26 + x = -26.134268691

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 = -26.134268691 + 26

Combine like terms: -26 + 26 = 0
0 + x = -26.134268691 + 26
x = -26.134268691 + 26

Combine like terms: -26.134268691 + 26 = -0.134268691
x = -0.134268691

Simplifying
x = -0.134268691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {52.134268691, -0.134268691}

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