3x(x+8)=13

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Solution for 3x(x+8)=13 equation: 


Simplifying
3x(x + 8) = 13

Reorder the terms:
3x(8 + x) = 13
(8 * 3x + x * 3x) = 13
(24x + 3x2) = 13

Solving
24x + 3x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 24x + 3x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 24x + 3x2 = 0

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

Divide each side by '3'.
-4.333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 8x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 8x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 8x + x2 = 0 + 4.333333333
8x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
8x + x2 = 4.333333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 4.333333333 + 16

Reorder the terms:
16 + 8x + x2 = 4.333333333 + 16

Combine like terms: 4.333333333 + 16 = 20.333333333
16 + 8x + x2 = 20.333333333

Factor a perfect square on the left side:
(x + 4)(x + 4) = 20.333333333

Calculate the square root of the right side: 4.509249753

Break this problem into two subproblems by setting 
(x + 4) equal to 4.509249753 and -4.509249753.


Subproblem 1
x + 4 = 4.509249753

Simplifying
x + 4 = 4.509249753

Reorder the terms:
4 + x = 4.509249753

Solving
4 + x = 4.509249753

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.509249753 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.509249753 + -4
x = 4.509249753 + -4

Combine like terms: 4.509249753 + -4 = 0.509249753
x = 0.509249753

Simplifying
x = 0.509249753


Subproblem 2
x + 4 = -4.509249753

Simplifying
x + 4 = -4.509249753

Reorder the terms:
4 + x = -4.509249753

Solving
4 + x = -4.509249753

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.509249753 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.509249753 + -4
x = -4.509249753 + -4

Combine like terms: -4.509249753 + -4 = -8.509249753
x = -8.509249753

Simplifying
x = -8.509249753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.509249753, -8.509249753}

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