x(x+15)=210

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Solution for x(x+15)=210 equation: 


Simplifying
x(x + 15) = 210

Reorder the terms:
x(15 + x) = 210
(15 * x + x * x) = 210
(15x + x2) = 210

Solving
15x + x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 15x + x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + 15x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + 15x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + 15x + x2 = 0 + 210
15x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
15x + x2 = 210

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 210 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 210 + 56.25

Combine like terms: 210 + 56.25 = 266.25
56.25 + 15x + x2 = 266.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 266.25

Calculate the square root of the right side: 16.317168872

Break this problem into two subproblems by setting 
(x + 7.5) equal to 16.317168872 and -16.317168872.


Subproblem 1
x + 7.5 = 16.317168872

Simplifying
x + 7.5 = 16.317168872

Reorder the terms:
7.5 + x = 16.317168872

Solving
7.5 + x = 16.317168872

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 16.317168872 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 16.317168872 + -7.5
x = 16.317168872 + -7.5

Combine like terms: 16.317168872 + -7.5 = 8.817168872
x = 8.817168872

Simplifying
x = 8.817168872


Subproblem 2
x + 7.5 = -16.317168872

Simplifying
x + 7.5 = -16.317168872

Reorder the terms:
7.5 + x = -16.317168872

Solving
7.5 + x = -16.317168872

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -16.317168872 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -16.317168872 + -7.5
x = -16.317168872 + -7.5

Combine like terms: -16.317168872 + -7.5 = -23.817168872
x = -23.817168872

Simplifying
x = -23.817168872


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.817168872, -23.817168872}

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