x(x+5)=105

Solution for x(x+5)=105 equation:

Simplifying
x(x + 5) = 105

Reorder the terms:
x(5 + x) = 105
(5 * x + x * x) = 105
(5x + x2) = 105

Solving
5x + x2 = 105

Solving for variable 'x'.

Reorder the terms:
-105 + 5x + x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 5x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 5x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 5x + x2 = 0 + 105
5x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
5x + x2 = 105

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 = 105 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 105 + 6.25

Combine like terms: 105 + 6.25 = 111.25
6.25 + 5x + x2 = 111.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.547511555 and -10.547511555.

Subproblem 1
x + 2.5 = 10.547511555

Simplifying
x + 2.5 = 10.547511555

Reorder the terms:
2.5 + x = 10.547511555

Solving
2.5 + x = 10.547511555

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 = 10.547511555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.547511555 + -2.5
x = 10.547511555 + -2.5

Combine like terms: 10.547511555 + -2.5 = 8.047511555
x = 8.047511555

Simplifying
x = 8.047511555

Subproblem 2
x + 2.5 = -10.547511555

Simplifying
x + 2.5 = -10.547511555

Reorder the terms:
2.5 + x = -10.547511555

Solving
2.5 + x = -10.547511555

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 = -10.547511555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.547511555 + -2.5
x = -10.547511555 + -2.5

Combine like terms: -10.547511555 + -2.5 = -13.047511555
x = -13.047511555

Simplifying
x = -13.047511555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.047511555, -13.047511555}