.5x(x+4)=16

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Solution for .5x(x+4)=16 equation:


Simplifying
0.5x(x + 4) = 16

Reorder the terms:
0.5x(4 + x) = 16
(4 * 0.5x + x * 0.5x) = 16
(2x + 0.5x2) = 16

Solving
2x + 0.5x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 2x + 0.5x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 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'.
-32 + 4x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 4x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 4x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 4x + x2 = 0 + 32
4x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
4x + x2 = 32

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 = 32 + 4

Reorder the terms:
4 + 4x + x2 = 32 + 4

Combine like terms: 32 + 4 = 36
4 + 4x + x2 = 36

Factor a perfect square on the left side:
(x + 2)(x + 2) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + 2) equal to 6 and -6.

Subproblem 1

x + 2 = 6 Simplifying x + 2 = 6 Reorder the terms: 2 + x = 6 Solving 2 + x = 6 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 = 6 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6 + -2 x = 6 + -2 Combine like terms: 6 + -2 = 4 x = 4 Simplifying x = 4

Subproblem 2

x + 2 = -6 Simplifying x + 2 = -6 Reorder the terms: 2 + x = -6 Solving 2 + x = -6 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 = -6 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6 + -2 x = -6 + -2 Combine like terms: -6 + -2 = -8 x = -8 Simplifying x = -8

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4, -8}

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