0.5(4x+8)(x)=20

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Solution for 0.5(4x+8)(x)=20 equation: 


Simplifying
0.5(4x + 8)(x) = 20

Reorder the terms:
0.5(8 + 4x)(x) = 20

Reorder the terms for easier multiplication:
0.5x(8 + 4x) = 20
(8 * 0.5x + 4x * 0.5x) = 20
(4x + 2x2) = 20

Solving
4x + 2x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 4x + 2x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + 2x + x2 = 0

Solving
-10 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2x + x2 = 0 + 10
2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
2x + x2 = 10

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 10 + 1

Reorder the terms:
1 + 2x + x2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2x + x2 = 11

Factor a perfect square on the left side:
(x + 1)(x + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 1) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 1 = 3.31662479

Simplifying
x + 1 = 3.31662479

Reorder the terms:
1 + x = 3.31662479

Solving
1 + x = 3.31662479

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.31662479 + -1
x = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
x = 2.31662479

Simplifying
x = 2.31662479


Subproblem 2
x + 1 = -3.31662479

Simplifying
x + 1 = -3.31662479

Reorder the terms:
1 + x = -3.31662479

Solving
1 + x = -3.31662479

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.31662479 + -1
x = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
x = -4.31662479

Simplifying
x = -4.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.31662479, -4.31662479}
Solution
x = {2.31662479, -4.31662479}

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