x(x+5)-15=1500

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Solution for x(x+5)-15=1500 equation: 


Simplifying
x(x + 5) + -15 = 1500

Reorder the terms:
x(5 + x) + -15 = 1500
(5 * x + x * x) + -15 = 1500
(5x + x2) + -15 = 1500

Reorder the terms:
-15 + 5x + x2 = 1500

Solving
-15 + 5x + x2 = 1500

Solving for variable 'x'.

Reorder the terms:
-15 + -1500 + 5x + x2 = 1500 + -1500

Combine like terms: -15 + -1500 = -1515
-1515 + 5x + x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
-1515 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1515' to each side of the equation.
-1515 + 5x + 1515 + x2 = 0 + 1515

Reorder the terms:
-1515 + 1515 + 5x + x2 = 0 + 1515

Combine like terms: -1515 + 1515 = 0
0 + 5x + x2 = 0 + 1515
5x + x2 = 0 + 1515

Combine like terms: 0 + 1515 = 1515
5x + x2 = 1515

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 = 1515 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1515 + 6.25

Combine like terms: 1515 + 6.25 = 1521.25
6.25 + 5x + x2 = 1521.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1521.25

Calculate the square root of the right side: 39.003204997

Break this problem into two subproblems by setting 
(x + 2.5) equal to 39.003204997 and -39.003204997.


Subproblem 1
x + 2.5 = 39.003204997

Simplifying
x + 2.5 = 39.003204997

Reorder the terms:
2.5 + x = 39.003204997

Solving
2.5 + x = 39.003204997

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 = 39.003204997 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 39.003204997 + -2.5
x = 39.003204997 + -2.5

Combine like terms: 39.003204997 + -2.5 = 36.503204997
x = 36.503204997

Simplifying
x = 36.503204997


Subproblem 2
x + 2.5 = -39.003204997

Simplifying
x + 2.5 = -39.003204997

Reorder the terms:
2.5 + x = -39.003204997

Solving
2.5 + x = -39.003204997

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 = -39.003204997 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -39.003204997 + -2.5
x = -39.003204997 + -2.5

Combine like terms: -39.003204997 + -2.5 = -41.503204997
x = -41.503204997

Simplifying
x = -41.503204997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.503204997, -41.503204997}

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