x^2+15x-264.75=0

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Solution for x^2+15x-264.75=0 equation: 


Simplifying
x2 + 15x + -264.75 = 0

Reorder the terms:
-264.75 + 15x + x2 = 0

Solving
-264.75 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '264.75' to each side of the equation.
-264.75 + 15x + 264.75 + x2 = 0 + 264.75

Reorder the terms:
-264.75 + 264.75 + 15x + x2 = 0 + 264.75

Combine like terms: -264.75 + 264.75 = 0.00
0.00 + 15x + x2 = 0 + 264.75
15x + x2 = 0 + 264.75

Combine like terms: 0 + 264.75 = 264.75
15x + x2 = 264.75

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 = 264.75 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 264.75 + 56.25

Combine like terms: 264.75 + 56.25 = 321
56.25 + 15x + x2 = 321

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 321

Calculate the square root of the right side: 17.916472867

Break this problem into two subproblems by setting 
(x + 7.5) equal to 17.916472867 and -17.916472867.


Subproblem 1
x + 7.5 = 17.916472867

Simplifying
x + 7.5 = 17.916472867

Reorder the terms:
7.5 + x = 17.916472867

Solving
7.5 + x = 17.916472867

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 = 17.916472867 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 17.916472867 + -7.5
x = 17.916472867 + -7.5

Combine like terms: 17.916472867 + -7.5 = 10.416472867
x = 10.416472867

Simplifying
x = 10.416472867


Subproblem 2
x + 7.5 = -17.916472867

Simplifying
x + 7.5 = -17.916472867

Reorder the terms:
7.5 + x = -17.916472867

Solving
7.5 + x = -17.916472867

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 = -17.916472867 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -17.916472867 + -7.5
x = -17.916472867 + -7.5

Combine like terms: -17.916472867 + -7.5 = -25.416472867
x = -25.416472867

Simplifying
x = -25.416472867


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.416472867, -25.416472867}

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