x^2-15x-199.75=0

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Solution for x^2-15x-199.75=0 equation: 


Simplifying
x2 + -15x + -199.75 = 0

Reorder the terms:
-199.75 + -15x + x2 = 0

Solving
-199.75 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '199.75' to each side of the equation.
-199.75 + -15x + 199.75 + x2 = 0 + 199.75

Reorder the terms:
-199.75 + 199.75 + -15x + x2 = 0 + 199.75

Combine like terms: -199.75 + 199.75 = 0.00
0.00 + -15x + x2 = 0 + 199.75
-15x + x2 = 0 + 199.75

Combine like terms: 0 + 199.75 = 199.75
-15x + x2 = 199.75

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 = 199.75 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 199.75 + 56.25

Combine like terms: 199.75 + 56.25 = 256
56.25 + -15x + x2 = 256

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 256

Calculate the square root of the right side: 16

Break this problem into two subproblems by setting 
(x + -7.5) equal to 16 and -16.


Subproblem 1
x + -7.5 = 16

Simplifying
x + -7.5 = 16

Reorder the terms:
-7.5 + x = 16

Solving
-7.5 + x = 16

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 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 16 + 7.5
x = 16 + 7.5

Combine like terms: 16 + 7.5 = 23.5
x = 23.5

Simplifying
x = 23.5


Subproblem 2
x + -7.5 = -16

Simplifying
x + -7.5 = -16

Reorder the terms:
-7.5 + x = -16

Solving
-7.5 + x = -16

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 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -16 + 7.5
x = -16 + 7.5

Combine like terms: -16 + 7.5 = -8.5
x = -8.5

Simplifying
x = -8.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.5, -8.5}

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