3x(x+5)=40

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Solution for 3x(x+5)=40 equation:


Simplifying
3x(x + 5) = 40

Reorder the terms:
3x(5 + x) = 40
(5 * 3x + x * 3x) = 40
(15x + 3x2) = 40

Solving
15x + 3x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 15x + 3x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 15x + 3x2 = 0

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

Divide each side by '3'.
-13.33333333 + 5x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + 5x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + 5x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + 5x + x2 = 0 + 13.33333333
5x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
5x + x2 = 13.33333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 13.33333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 13.33333333 + 6.25

Combine like terms: 13.33333333 + 6.25 = 19.58333333
6.25 + 5x + x2 = 19.58333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 19.58333333

Calculate the square root of the right side: 4.425306015

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.425306015 and -4.425306015.


Subproblem 1
x + 2.5 = 4.425306015

Simplifying
x + 2.5 = 4.425306015

Reorder the terms:
2.5 + x = 4.425306015

Solving
2.5 + x = 4.425306015

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.425306015 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.425306015 + -2.5
x = 4.425306015 + -2.5

Combine like terms: 4.425306015 + -2.5 = 1.925306015
x = 1.925306015

Simplifying
x = 1.925306015


Subproblem 2
x + 2.5 = -4.425306015

Simplifying
x + 2.5 = -4.425306015

Reorder the terms:
2.5 + x = -4.425306015

Solving
2.5 + x = -4.425306015

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.425306015 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.425306015 + -2.5
x = -4.425306015 + -2.5

Combine like terms: -4.425306015 + -2.5 = -6.925306015
x = -6.925306015

Simplifying
x = -6.925306015


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.925306015, -6.925306015}

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