88=.5(x)(x+5)

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Solution for 88=.5(x)(x+5) equation: 


Simplifying
88 = 0.5(x)(x + 5)

Reorder the terms:
88 = 0.5x(5 + x)
88 = (5 * 0.5x + x * 0.5x)
88 = (2.5x + 0.5x2)

Solving
88 = 2.5x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
88 + -2.5x + -0.5x2 = 2.5x + -2.5x + 0.5x2 + -0.5x2

Combine like terms: 2.5x + -2.5x = 0.0
88 + -2.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
88 + -2.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
88 + -2.5x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-176 + 5x + x2 = 0

Move the constant term to the right:

Add '176' to each side of the equation.
-176 + 5x + 176 + x2 = 0 + 176

Reorder the terms:
-176 + 176 + 5x + x2 = 0 + 176

Combine like terms: -176 + 176 = 0
0 + 5x + x2 = 0 + 176
5x + x2 = 0 + 176

Combine like terms: 0 + 176 = 176
5x + x2 = 176

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 = 176 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 176 + 6.25

Combine like terms: 176 + 6.25 = 182.25
6.25 + 5x + x2 = 182.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 182.25

Calculate the square root of the right side: 13.5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.5 and -13.5.


Subproblem 1
x + 2.5 = 13.5

Simplifying
x + 2.5 = 13.5

Reorder the terms:
2.5 + x = 13.5

Solving
2.5 + x = 13.5

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 = 13.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 13.5 + -2.5
x = 13.5 + -2.5

Combine like terms: 13.5 + -2.5 = 11
x = 11

Simplifying
x = 11


Subproblem 2
x + 2.5 = -13.5

Simplifying
x + 2.5 = -13.5

Reorder the terms:
2.5 + x = -13.5

Solving
2.5 + x = -13.5

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 = -13.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -13.5 + -2.5
x = -13.5 + -2.5

Combine like terms: -13.5 + -2.5 = -16
x = -16

Simplifying
x = -16


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11, -16}

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