(x+5)(-x-5)+12.25=0

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Solution for (x+5)(-x-5)+12.25=0 equation: 


Simplifying
(x + 5)(-1x + -5) + 12.25 = 0

Reorder the terms:
(5 + x)(-1x + -5) + 12.25 = 0

Reorder the terms:
(5 + x)(-5 + -1x) + 12.25 = 0

Multiply (5 + x) * (-5 + -1x)
(5(-5 + -1x) + x(-5 + -1x)) + 12.25 = 0
((-5 * 5 + -1x * 5) + x(-5 + -1x)) + 12.25 = 0
((-25 + -5x) + x(-5 + -1x)) + 12.25 = 0
(-25 + -5x + (-5 * x + -1x * x)) + 12.25 = 0
(-25 + -5x + (-5x + -1x2)) + 12.25 = 0

Combine like terms: -5x + -5x = -10x
(-25 + -10x + -1x2) + 12.25 = 0

Reorder the terms:
-25 + 12.25 + -10x + -1x2 = 0

Combine like terms: -25 + 12.25 = -12.75
-12.75 + -10x + -1x2 = 0

Solving
-12.75 + -10x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
12.75 + 10x + x2 = 0

Move the constant term to the right:

Add '-12.75' to each side of the equation.
12.75 + 10x + -12.75 + x2 = 0 + -12.75

Reorder the terms:
12.75 + -12.75 + 10x + x2 = 0 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + 10x + x2 = 0 + -12.75
10x + x2 = 0 + -12.75

Combine like terms: 0 + -12.75 = -12.75
10x + x2 = -12.75

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 = -12.75 + 25

Reorder the terms:
25 + 10x + x2 = -12.75 + 25

Combine like terms: -12.75 + 25 = 12.25
25 + 10x + x2 = 12.25

Factor a perfect square on the left side:
(x + 5)(x + 5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + 5) equal to 3.5 and -3.5.


Subproblem 1
x + 5 = 3.5

Simplifying
x + 5 = 3.5

Reorder the terms:
5 + x = 3.5

Solving
5 + x = 3.5

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 = 3.5 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.5 + -5
x = 3.5 + -5

Combine like terms: 3.5 + -5 = -1.5
x = -1.5

Simplifying
x = -1.5


Subproblem 2
x + 5 = -3.5

Simplifying
x + 5 = -3.5

Reorder the terms:
5 + x = -3.5

Solving
5 + x = -3.5

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 = -3.5 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.5 + -5
x = -3.5 + -5

Combine like terms: -3.5 + -5 = -8.5
x = -8.5

Simplifying
x = -8.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -8.5}

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