0.5*x*(x+4)=30

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Solution for 0.5*x*(x+4)=30 equation: 


Simplifying
0.5x(x + 4) = 30

Reorder the terms:
0.5x(4 + x) = 30
(4 * 0.5x + x * 0.5x) = 30
(2x + 0.5x2) = 30

Solving
2x + 0.5x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 2x + 0.5x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 2x + 0.5x2 = 0

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

Divide each side by '0.5'.
-60 + 4x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 4x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 4x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 4x + x2 = 0 + 60
4x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
4x + x2 = 60

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 = 60 + 4

Reorder the terms:
4 + 4x + x2 = 60 + 4

Combine like terms: 60 + 4 = 64
4 + 4x + x2 = 64

Factor a perfect square on the left side:
(x + 2)(x + 2) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + 2) equal to 8 and -8.


Subproblem 1
x + 2 = 8

Simplifying
x + 2 = 8

Reorder the terms:
2 + x = 8

Solving
2 + x = 8

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 = 8 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8 + -2
x = 8 + -2

Combine like terms: 8 + -2 = 6
x = 6

Simplifying
x = 6


Subproblem 2
x + 2 = -8

Simplifying
x + 2 = -8

Reorder the terms:
2 + x = -8

Solving
2 + x = -8

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 = -8 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8 + -2
x = -8 + -2

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

Simplifying
x = -10


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, -10}

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