(x)(x+5)=95

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Solution for (x)(x+5)=95 equation: 


Simplifying
(x)(x + 5) = 95

Reorder the terms:
x(5 + x) = 95
(5 * x + x * x) = 95
(5x + x2) = 95

Solving
5x + x2 = 95

Solving for variable 'x'.

Reorder the terms:
-95 + 5x + x2 = 95 + -95

Combine like terms: 95 + -95 = 0
-95 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '95' to each side of the equation.
-95 + 5x + 95 + x2 = 0 + 95

Reorder the terms:
-95 + 95 + 5x + x2 = 0 + 95

Combine like terms: -95 + 95 = 0
0 + 5x + x2 = 0 + 95
5x + x2 = 0 + 95

Combine like terms: 0 + 95 = 95
5x + x2 = 95

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 95 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 95 + 6.25

Combine like terms: 95 + 6.25 = 101.25
6.25 + 5x + x2 = 101.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.062305899 and -10.062305899.


Subproblem 1
x + 2.5 = 10.062305899

Simplifying
x + 2.5 = 10.062305899

Reorder the terms:
2.5 + x = 10.062305899

Solving
2.5 + x = 10.062305899

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 10.062305899 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.062305899 + -2.5
x = 10.062305899 + -2.5

Combine like terms: 10.062305899 + -2.5 = 7.562305899
x = 7.562305899

Simplifying
x = 7.562305899


Subproblem 2
x + 2.5 = -10.062305899

Simplifying
x + 2.5 = -10.062305899

Reorder the terms:
2.5 + x = -10.062305899

Solving
2.5 + x = -10.062305899

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -10.062305899 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.062305899 + -2.5
x = -10.062305899 + -2.5

Combine like terms: -10.062305899 + -2.5 = -12.562305899
x = -12.562305899

Simplifying
x = -12.562305899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.562305899, -12.562305899}

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