x^2-10x-25=21-25

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Solution for x^2-10x-25=21-25 equation: 


Simplifying
x2 + -10x + -25 = 21 + -25

Reorder the terms:
-25 + -10x + x2 = 21 + -25

Combine like terms: 21 + -25 = -4
-25 + -10x + x2 = -4

Solving
-25 + -10x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
-25 + 4 + -10x + x2 = -4 + 4

Combine like terms: -25 + 4 = -21
-21 + -10x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
-21 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -10x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -10x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -10x + x2 = 0 + 21
-10x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-10x + x2 = 21

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 = 21 + 25

Reorder the terms:
25 + -10x + x2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + -10x + x2 = 46

Factor a perfect square on the left side:
(x + -5)(x + -5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + -5) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + -5 = 6.782329983

Simplifying
x + -5 = 6.782329983

Reorder the terms:
-5 + x = 6.782329983

Solving
-5 + x = 6.782329983

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 = 6.782329983 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.782329983 + 5
x = 6.782329983 + 5

Combine like terms: 6.782329983 + 5 = 11.782329983
x = 11.782329983

Simplifying
x = 11.782329983


Subproblem 2
x + -5 = -6.782329983

Simplifying
x + -5 = -6.782329983

Reorder the terms:
-5 + x = -6.782329983

Solving
-5 + x = -6.782329983

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 = -6.782329983 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.782329983 + 5
x = -6.782329983 + 5

Combine like terms: -6.782329983 + 5 = -1.782329983
x = -1.782329983

Simplifying
x = -1.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.782329983, -1.782329983}

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