2x(5+8x)=36

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Solution for 2x(5+8x)=36 equation: 


Simplifying
2x(5 + 8x) = 36
(5 * 2x + 8x * 2x) = 36
(10x + 16x2) = 36

Solving
10x + 16x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 10x + 16x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 10x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 5x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-18 + 5x + 8x2)' equal to zero and attempt to solve:

Simplifying
-18 + 5x + 8x2 = 0

Solving
-18 + 5x + 8x2 = 0

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

Divide each side by '8'.
-2.25 + 0.625x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.625x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.625x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.625x + x2 = 0 + 2.25
0.625x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.625x + x2 = 2.25

The x term is 0.625x.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625x + 0.09765625 + x2 = 2.25 + 0.09765625

Reorder the terms:
0.09765625 + 0.625x + x2 = 2.25 + 0.09765625

Combine like terms: 2.25 + 0.09765625 = 2.34765625
0.09765625 + 0.625x + x2 = 2.34765625

Factor a perfect square on the left side:
(x + 0.3125)(x + 0.3125) = 2.34765625

Calculate the square root of the right side: 1.532206334

Break this problem into two subproblems by setting 
(x + 0.3125) equal to 1.532206334 and -1.532206334.


Subproblem 1
x + 0.3125 = 1.532206334

Simplifying
x + 0.3125 = 1.532206334

Reorder the terms:
0.3125 + x = 1.532206334

Solving
0.3125 + x = 1.532206334

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = 1.532206334 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = 1.532206334 + -0.3125
x = 1.532206334 + -0.3125

Combine like terms: 1.532206334 + -0.3125 = 1.219706334
x = 1.219706334

Simplifying
x = 1.219706334


Subproblem 2
x + 0.3125 = -1.532206334

Simplifying
x + 0.3125 = -1.532206334

Reorder the terms:
0.3125 + x = -1.532206334

Solving
0.3125 + x = -1.532206334

Solving for variable 'x'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + x = -1.532206334 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + x = -1.532206334 + -0.3125
x = -1.532206334 + -0.3125

Combine like terms: -1.532206334 + -0.3125 = -1.844706334
x = -1.844706334

Simplifying
x = -1.844706334


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.219706334, -1.844706334}
Solution
x = {1.219706334, -1.844706334}

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