x(x+5)=65

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Solution for x(x+5)=65 equation: 


Simplifying
x(x + 5) = 65

Reorder the terms:
x(5 + x) = 65
(5 * x + x * x) = 65
(5x + x2) = 65

Solving
5x + x2 = 65

Solving for variable 'x'.

Reorder the terms:
-65 + 5x + x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 5x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + 5x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 5x + x2 = 0 + 65
5x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
5x + x2 = 65

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 = 65 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 65 + 6.25

Combine like terms: 65 + 6.25 = 71.25
6.25 + 5x + x2 = 71.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 71.25

Calculate the square root of the right side: 8.440971508

Break this problem into two subproblems by setting 
(x + 2.5) equal to 8.440971508 and -8.440971508.


Subproblem 1
x + 2.5 = 8.440971508

Simplifying
x + 2.5 = 8.440971508

Reorder the terms:
2.5 + x = 8.440971508

Solving
2.5 + x = 8.440971508

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 = 8.440971508 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 8.440971508 + -2.5
x = 8.440971508 + -2.5

Combine like terms: 8.440971508 + -2.5 = 5.940971508
x = 5.940971508

Simplifying
x = 5.940971508


Subproblem 2
x + 2.5 = -8.440971508

Simplifying
x + 2.5 = -8.440971508

Reorder the terms:
2.5 + x = -8.440971508

Solving
2.5 + x = -8.440971508

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 = -8.440971508 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -8.440971508 + -2.5
x = -8.440971508 + -2.5

Combine like terms: -8.440971508 + -2.5 = -10.940971508
x = -10.940971508

Simplifying
x = -10.940971508


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.940971508, -10.940971508}

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