x(x-15)=252

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Solution for x(x-15)=252 equation: 


Simplifying
x(x + -15) = 252

Reorder the terms:
x(-15 + x) = 252
(-15 * x + x * x) = 252
(-15x + x2) = 252

Solving
-15x + x2 = 252

Solving for variable 'x'.

Reorder the terms:
-252 + -15x + x2 = 252 + -252

Combine like terms: 252 + -252 = 0
-252 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '252' to each side of the equation.
-252 + -15x + 252 + x2 = 0 + 252

Reorder the terms:
-252 + 252 + -15x + x2 = 0 + 252

Combine like terms: -252 + 252 = 0
0 + -15x + x2 = 0 + 252
-15x + x2 = 0 + 252

Combine like terms: 0 + 252 = 252
-15x + x2 = 252

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 = 252 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 252 + 56.25

Combine like terms: 252 + 56.25 = 308.25
56.25 + -15x + x2 = 308.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 308.25

Calculate the square root of the right side: 17.557049866

Break this problem into two subproblems by setting 
(x + -7.5) equal to 17.557049866 and -17.557049866.


Subproblem 1
x + -7.5 = 17.557049866

Simplifying
x + -7.5 = 17.557049866

Reorder the terms:
-7.5 + x = 17.557049866

Solving
-7.5 + x = 17.557049866

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 = 17.557049866 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 17.557049866 + 7.5
x = 17.557049866 + 7.5

Combine like terms: 17.557049866 + 7.5 = 25.057049866
x = 25.057049866

Simplifying
x = 25.057049866


Subproblem 2
x + -7.5 = -17.557049866

Simplifying
x + -7.5 = -17.557049866

Reorder the terms:
-7.5 + x = -17.557049866

Solving
-7.5 + x = -17.557049866

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 = -17.557049866 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -17.557049866 + 7.5
x = -17.557049866 + 7.5

Combine like terms: -17.557049866 + 7.5 = -10.057049866
x = -10.057049866

Simplifying
x = -10.057049866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.057049866, -10.057049866}

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