(x+5)x=225

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Solution for (x+5)x=225 equation: 


Simplifying
(x + 5) * x = 225

Reorder the terms:
(5 + x) * x = 225

Reorder the terms for easier multiplication:
x(5 + x) = 225
(5 * x + x * x) = 225
(5x + x2) = 225

Solving
5x + x2 = 225

Solving for variable 'x'.

Reorder the terms:
-225 + 5x + x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 5x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 5x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 5x + x2 = 0 + 225
5x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
5x + x2 = 225

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 = 225 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 225 + 6.25

Combine like terms: 225 + 6.25 = 231.25
6.25 + 5x + x2 = 231.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(x + 2.5) equal to 15.206906326 and -15.206906326.


Subproblem 1
x + 2.5 = 15.206906326

Simplifying
x + 2.5 = 15.206906326

Reorder the terms:
2.5 + x = 15.206906326

Solving
2.5 + x = 15.206906326

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 = 15.206906326 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 15.206906326 + -2.5
x = 15.206906326 + -2.5

Combine like terms: 15.206906326 + -2.5 = 12.706906326
x = 12.706906326

Simplifying
x = 12.706906326


Subproblem 2
x + 2.5 = -15.206906326

Simplifying
x + 2.5 = -15.206906326

Reorder the terms:
2.5 + x = -15.206906326

Solving
2.5 + x = -15.206906326

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 = -15.206906326 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -15.206906326 + -2.5
x = -15.206906326 + -2.5

Combine like terms: -15.206906326 + -2.5 = -17.706906326
x = -17.706906326

Simplifying
x = -17.706906326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.706906326, -17.706906326}

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