x(5+3x)=32

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Solution for x(5+3x)=32 equation: 


Simplifying
x(5 + 3x) = 32
(5 * x + 3x * x) = 32
(5x + 3x2) = 32

Solving
5x + 3x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 5x + 3x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 5x + 3x2 = 0

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

Divide each side by '3'.
-10.66666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + 1.666666667x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + 1.666666667x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + 1.666666667x + x2 = 0 + 10.66666667
1.666666667x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
1.666666667x + x2 = 10.66666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 10.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 10.66666667 + 0.6944444447

Combine like terms: 10.66666667 + 0.6944444447 = 11.3611111147
0.6944444447 + 1.666666667x + x2 = 11.3611111147

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 11.3611111147

Calculate the square root of the right side: 3.370624737

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 3.370624737 and -3.370624737.


Subproblem 1
x + 0.8333333335 = 3.370624737

Simplifying
x + 0.8333333335 = 3.370624737

Reorder the terms:
0.8333333335 + x = 3.370624737

Solving
0.8333333335 + x = 3.370624737

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 3.370624737 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 3.370624737 + -0.8333333335
x = 3.370624737 + -0.8333333335

Combine like terms: 3.370624737 + -0.8333333335 = 2.5372914035
x = 2.5372914035

Simplifying
x = 2.5372914035


Subproblem 2
x + 0.8333333335 = -3.370624737

Simplifying
x + 0.8333333335 = -3.370624737

Reorder the terms:
0.8333333335 + x = -3.370624737

Solving
0.8333333335 + x = -3.370624737

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -3.370624737 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -3.370624737 + -0.8333333335
x = -3.370624737 + -0.8333333335

Combine like terms: -3.370624737 + -0.8333333335 = -4.2039580705
x = -4.2039580705

Simplifying
x = -4.2039580705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5372914035, -4.2039580705}

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