2x(5x+1)=32

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Solution for 2x(5x+1)=32 equation: 


Simplifying
2x(5x + 1) = 32

Reorder the terms:
2x(1 + 5x) = 32
(1 * 2x + 5x * 2x) = 32
(2x + 10x2) = 32

Solving
2x + 10x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 2x + 10x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 2x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + x + 5x2)' equal to zero and attempt to solve:

Simplifying
-16 + x + 5x2 = 0

Solving
-16 + x + 5x2 = 0

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

Divide each side by '5'.
-3.2 + 0.2x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 0.2x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 0.2x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 0.2x + x2 = 0 + 3.2
0.2x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
0.2x + x2 = 3.2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2x + 0.25 + x2 = 3.2 + 0.25

Reorder the terms:
0.25 + 0.2x + x2 = 3.2 + 0.25

Combine like terms: 3.2 + 0.25 = 3.45
0.25 + 0.2x + x2 = 3.45

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.45

Calculate the square root of the right side: 1.857417562

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.857417562 and -1.857417562.


Subproblem 1
x + 0.5 = 1.857417562

Simplifying
x + 0.5 = 1.857417562

Reorder the terms:
0.5 + x = 1.857417562

Solving
0.5 + x = 1.857417562

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.857417562 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.857417562 + -0.5
x = 1.857417562 + -0.5

Combine like terms: 1.857417562 + -0.5 = 1.357417562
x = 1.357417562

Simplifying
x = 1.357417562


Subproblem 2
x + 0.5 = -1.857417562

Simplifying
x + 0.5 = -1.857417562

Reorder the terms:
0.5 + x = -1.857417562

Solving
0.5 + x = -1.857417562

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.857417562 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.857417562 + -0.5
x = -1.857417562 + -0.5

Combine like terms: -1.857417562 + -0.5 = -2.357417562
x = -2.357417562

Simplifying
x = -2.357417562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.357417562, -2.357417562}
Solution
x = {1.357417562, -2.357417562}

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