x(x-1)+5x=40

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Solution for x(x-1)+5x=40 equation: 


Simplifying
x(x + -1) + 5x = 40

Reorder the terms:
x(-1 + x) + 5x = 40
(-1 * x + x * x) + 5x = 40
(-1x + x2) + 5x = 40

Reorder the terms:
-1x + 5x + x2 = 40

Combine like terms: -1x + 5x = 4x
4x + x2 = 40

Solving
4x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 4x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 4x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 4x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 4x + x2 = 0 + 40
4x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
4x + x2 = 40

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 40 + 4

Reorder the terms:
4 + 4x + x2 = 40 + 4

Combine like terms: 40 + 4 = 44
4 + 4x + x2 = 44

Factor a perfect square on the left side:
(x + 2)(x + 2) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + 2) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + 2 = 6.633249581

Simplifying
x + 2 = 6.633249581

Reorder the terms:
2 + x = 6.633249581

Solving
2 + x = 6.633249581

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.633249581 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.633249581 + -2
x = 6.633249581 + -2

Combine like terms: 6.633249581 + -2 = 4.633249581
x = 4.633249581

Simplifying
x = 4.633249581


Subproblem 2
x + 2 = -6.633249581

Simplifying
x + 2 = -6.633249581

Reorder the terms:
2 + x = -6.633249581

Solving
2 + x = -6.633249581

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.633249581 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.633249581 + -2
x = -6.633249581 + -2

Combine like terms: -6.633249581 + -2 = -8.633249581
x = -8.633249581

Simplifying
x = -8.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.633249581, -8.633249581}

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