x(x+5)=40

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


Simplifying
x(x + 5) = 40

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

Solving
5x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 5x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 5x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 5x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 5x + x2 = 0 + 40
5x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
5x + x2 = 40

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 = 40 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 40 + 6.25

Combine like terms: 40 + 6.25 = 46.25
6.25 + 5x + x2 = 46.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
x + 2.5 = 6.800735254

Simplifying
x + 2.5 = 6.800735254

Reorder the terms:
2.5 + x = 6.800735254

Solving
2.5 + x = 6.800735254

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 = 6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.800735254 + -2.5
x = 6.800735254 + -2.5

Combine like terms: 6.800735254 + -2.5 = 4.300735254
x = 4.300735254

Simplifying
x = 4.300735254


Subproblem 2
x + 2.5 = -6.800735254

Simplifying
x + 2.5 = -6.800735254

Reorder the terms:
2.5 + x = -6.800735254

Solving
2.5 + x = -6.800735254

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 = -6.800735254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.800735254 + -2.5
x = -6.800735254 + -2.5

Combine like terms: -6.800735254 + -2.5 = -9.300735254
x = -9.300735254

Simplifying
x = -9.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.300735254, -9.300735254}

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