8x(5x+2)=16

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Solution for 8x(5x+2)=16 equation: 


Simplifying
8x(5x + 2) = 16

Reorder the terms:
8x(2 + 5x) = 16
(2 * 8x + 5x * 8x) = 16
(16x + 40x2) = 16

Solving
16x + 40x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 16x + 40x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 16x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + 2x + 5x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-2 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + 2x + 5x2 = 0

Solving
-2 + 2x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 0.4x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.4x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.4x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.4x + x2 = 0 + 0.4
0.4x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.4x + x2 = 0.4

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.4 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.4 + 0.04

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + 0.4x + x2 = 0.44

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.663324958 and -0.663324958.


Subproblem 1
x + 0.2 = 0.663324958

Simplifying
x + 0.2 = 0.663324958

Reorder the terms:
0.2 + x = 0.663324958

Solving
0.2 + x = 0.663324958

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 0.663324958 + -0.2
x = 0.663324958 + -0.2

Combine like terms: 0.663324958 + -0.2 = 0.463324958
x = 0.463324958

Simplifying
x = 0.463324958


Subproblem 2
x + 0.2 = -0.663324958

Simplifying
x + 0.2 = -0.663324958

Reorder the terms:
0.2 + x = -0.663324958

Solving
0.2 + x = -0.663324958

Solving for variable 'x'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -0.663324958 + -0.2
x = -0.663324958 + -0.2

Combine like terms: -0.663324958 + -0.2 = -0.863324958
x = -0.863324958

Simplifying
x = -0.863324958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.463324958, -0.863324958}
Solution
x = {0.463324958, -0.863324958}

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