x^2-10x-252=0

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Solution for x^2-10x-252=0 equation: 


Simplifying
x2 + -10x + -252 = 0

Reorder the terms:
-252 + -10x + x2 = 0

Solving
-252 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '252' to each side of the equation.
-252 + -10x + 252 + x2 = 0 + 252

Reorder the terms:
-252 + 252 + -10x + x2 = 0 + 252

Combine like terms: -252 + 252 = 0
0 + -10x + x2 = 0 + 252
-10x + x2 = 0 + 252

Combine like terms: 0 + 252 = 252
-10x + x2 = 252

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 = 252 + 25

Reorder the terms:
25 + -10x + x2 = 252 + 25

Combine like terms: 252 + 25 = 277
25 + -10x + x2 = 277

Factor a perfect square on the left side:
(x + -5)(x + -5) = 277

Calculate the square root of the right side: 16.643316977

Break this problem into two subproblems by setting 
(x + -5) equal to 16.643316977 and -16.643316977.


Subproblem 1
x + -5 = 16.643316977

Simplifying
x + -5 = 16.643316977

Reorder the terms:
-5 + x = 16.643316977

Solving
-5 + x = 16.643316977

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 = 16.643316977 + 5

Combine like terms: -5 + 5 = 0
0 + x = 16.643316977 + 5
x = 16.643316977 + 5

Combine like terms: 16.643316977 + 5 = 21.643316977
x = 21.643316977

Simplifying
x = 21.643316977


Subproblem 2
x + -5 = -16.643316977

Simplifying
x + -5 = -16.643316977

Reorder the terms:
-5 + x = -16.643316977

Solving
-5 + x = -16.643316977

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 = -16.643316977 + 5

Combine like terms: -5 + 5 = 0
0 + x = -16.643316977 + 5
x = -16.643316977 + 5

Combine like terms: -16.643316977 + 5 = -11.643316977
x = -11.643316977

Simplifying
x = -11.643316977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.643316977, -11.643316977}

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