x(x+5)=218

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Solution for x(x+5)=218 equation: 


Simplifying
x(x + 5) = 218

Reorder the terms:
x(5 + x) = 218
(5 * x + x * x) = 218
(5x + x2) = 218

Solving
5x + x2 = 218

Solving for variable 'x'.

Reorder the terms:
-218 + 5x + x2 = 218 + -218

Combine like terms: 218 + -218 = 0
-218 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '218' to each side of the equation.
-218 + 5x + 218 + x2 = 0 + 218

Reorder the terms:
-218 + 218 + 5x + x2 = 0 + 218

Combine like terms: -218 + 218 = 0
0 + 5x + x2 = 0 + 218
5x + x2 = 0 + 218

Combine like terms: 0 + 218 = 218
5x + x2 = 218

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 = 218 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 218 + 6.25

Combine like terms: 218 + 6.25 = 224.25
6.25 + 5x + x2 = 224.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 224.25

Calculate the square root of the right side: 14.974979132

Break this problem into two subproblems by setting 
(x + 2.5) equal to 14.974979132 and -14.974979132.


Subproblem 1
x + 2.5 = 14.974979132

Simplifying
x + 2.5 = 14.974979132

Reorder the terms:
2.5 + x = 14.974979132

Solving
2.5 + x = 14.974979132

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 = 14.974979132 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 14.974979132 + -2.5
x = 14.974979132 + -2.5

Combine like terms: 14.974979132 + -2.5 = 12.474979132
x = 12.474979132

Simplifying
x = 12.474979132


Subproblem 2
x + 2.5 = -14.974979132

Simplifying
x + 2.5 = -14.974979132

Reorder the terms:
2.5 + x = -14.974979132

Solving
2.5 + x = -14.974979132

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 = -14.974979132 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -14.974979132 + -2.5
x = -14.974979132 + -2.5

Combine like terms: -14.974979132 + -2.5 = -17.474979132
x = -17.474979132

Simplifying
x = -17.474979132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.474979132, -17.474979132}

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