8x(5x+8)=10

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Solution for 8x(5x+8)=10 equation: 


Simplifying
8x(5x + 8) = 10

Reorder the terms:
8x(8 + 5x) = 10
(8 * 8x + 5x * 8x) = 10
(64x + 40x2) = 10

Solving
64x + 40x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 64x + 40x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 64x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 32x + 20x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 32x + 20x2)' equal to zero and attempt to solve:

Simplifying
-5 + 32x + 20x2 = 0

Solving
-5 + 32x + 20x2 = 0

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

Divide each side by '20'.
-0.25 + 1.6x + x2 = 0.0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.6x + 0.25 + x2 = 0.0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.6x + x2 = 0.0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.6x + x2 = 0.0 + 0.25
1.6x + x2 = 0.0 + 0.25

Combine like terms: 0.0 + 0.25 = 0.25
1.6x + x2 = 0.25

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.25 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.25 + 0.64

Combine like terms: 0.25 + 0.64 = 0.89
0.64 + 1.6x + x2 = 0.89

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + 0.8) equal to 0.943398113 and -0.943398113.


Subproblem 1
x + 0.8 = 0.943398113

Simplifying
x + 0.8 = 0.943398113

Reorder the terms:
0.8 + x = 0.943398113

Solving
0.8 + x = 0.943398113

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 0.943398113 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 0.943398113 + -0.8
x = 0.943398113 + -0.8

Combine like terms: 0.943398113 + -0.8 = 0.143398113
x = 0.143398113

Simplifying
x = 0.143398113


Subproblem 2
x + 0.8 = -0.943398113

Simplifying
x + 0.8 = -0.943398113

Reorder the terms:
0.8 + x = -0.943398113

Solving
0.8 + x = -0.943398113

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -0.943398113 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -0.943398113 + -0.8
x = -0.943398113 + -0.8

Combine like terms: -0.943398113 + -0.8 = -1.743398113
x = -1.743398113

Simplifying
x = -1.743398113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.143398113, -1.743398113}
Solution
x = {0.143398113, -1.743398113}

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