48=.5(x)(x+4)

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Solution for 48=.5(x)(x+4) equation: 


Simplifying
48 = 0.5(x)(x + 4)

Reorder the terms:
48 = 0.5x(4 + x)
48 = (4 * 0.5x + x * 0.5x)
48 = (2x + 0.5x2)

Solving
48 = 2x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
48 + -2x + -0.5x2 = 2x + -2x + 0.5x2 + -0.5x2

Combine like terms: 2x + -2x = 0
48 + -2x + -0.5x2 = 0 + 0.5x2 + -0.5x2
48 + -2x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
48 + -2x + -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'.
-96 + 4x + x2 = 0

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 4x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 4x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 4x + x2 = 0 + 96
4x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
4x + x2 = 96

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 96 + 4

Reorder the terms:
4 + 4x + x2 = 96 + 4

Combine like terms: 96 + 4 = 100
4 + 4x + x2 = 100

Factor a perfect square on the left side:
(x + 2)(x + 2) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(x + 2) equal to 10 and -10.


Subproblem 1
x + 2 = 10

Simplifying
x + 2 = 10

Reorder the terms:
2 + x = 10

Solving
2 + x = 10

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 10 + -2

Combine like terms: 2 + -2 = 0
0 + x = 10 + -2
x = 10 + -2

Combine like terms: 10 + -2 = 8
x = 8

Simplifying
x = 8


Subproblem 2
x + 2 = -10

Simplifying
x + 2 = -10

Reorder the terms:
2 + x = -10

Solving
2 + x = -10

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -10 + -2

Combine like terms: 2 + -2 = 0
0 + x = -10 + -2
x = -10 + -2

Combine like terms: -10 + -2 = -12
x = -12

Simplifying
x = -12


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, -12}

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