x(x+5)=85

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Solution for x(x+5)=85 equation: 


Simplifying
x(x + 5) = 85

Reorder the terms:
x(5 + x) = 85
(5 * x + x * x) = 85
(5x + x2) = 85

Solving
5x + x2 = 85

Solving for variable 'x'.

Reorder the terms:
-85 + 5x + x2 = 85 + -85

Combine like terms: 85 + -85 = 0
-85 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 5x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 5x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 5x + x2 = 0 + 85
5x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
5x + x2 = 85

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 = 85 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 85 + 6.25

Combine like terms: 85 + 6.25 = 91.25
6.25 + 5x + x2 = 91.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 91.25

Calculate the square root of the right side: 9.552486587

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.552486587 and -9.552486587.


Subproblem 1
x + 2.5 = 9.552486587

Simplifying
x + 2.5 = 9.552486587

Reorder the terms:
2.5 + x = 9.552486587

Solving
2.5 + x = 9.552486587

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 = 9.552486587 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.552486587 + -2.5
x = 9.552486587 + -2.5

Combine like terms: 9.552486587 + -2.5 = 7.052486587
x = 7.052486587

Simplifying
x = 7.052486587


Subproblem 2
x + 2.5 = -9.552486587

Simplifying
x + 2.5 = -9.552486587

Reorder the terms:
2.5 + x = -9.552486587

Solving
2.5 + x = -9.552486587

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 = -9.552486587 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.552486587 + -2.5
x = -9.552486587 + -2.5

Combine like terms: -9.552486587 + -2.5 = -12.052486587
x = -12.052486587

Simplifying
x = -12.052486587


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.052486587, -12.052486587}

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