x^2-10x-52=0

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Solution for x^2-10x-52=0 equation: 


Simplifying
x2 + -10x + -52 = 0

Reorder the terms:
-52 + -10x + x2 = 0

Solving
-52 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -10x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + -10x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -10x + x2 = 0 + 52
-10x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
-10x + x2 = 52

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 52 + 25

Reorder the terms:
25 + -10x + x2 = 52 + 25

Combine like terms: 52 + 25 = 77
25 + -10x + x2 = 77

Factor a perfect square on the left side:
(x + -5)(x + -5) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(x + -5) equal to 8.774964387 and -8.774964387.


Subproblem 1
x + -5 = 8.774964387

Simplifying
x + -5 = 8.774964387

Reorder the terms:
-5 + x = 8.774964387

Solving
-5 + x = 8.774964387

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 8.774964387 + 5

Combine like terms: -5 + 5 = 0
0 + x = 8.774964387 + 5
x = 8.774964387 + 5

Combine like terms: 8.774964387 + 5 = 13.774964387
x = 13.774964387

Simplifying
x = 13.774964387


Subproblem 2
x + -5 = -8.774964387

Simplifying
x + -5 = -8.774964387

Reorder the terms:
-5 + x = -8.774964387

Solving
-5 + x = -8.774964387

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -8.774964387 + 5

Combine like terms: -5 + 5 = 0
0 + x = -8.774964387 + 5
x = -8.774964387 + 5

Combine like terms: -8.774964387 + 5 = -3.774964387
x = -3.774964387

Simplifying
x = -3.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.774964387, -3.774964387}

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