-x^2+15x+44=0

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Solution for -x^2+15x+44=0 equation:


Simplifying
-1x2 + 15x + 44 = 0

Reorder the terms:
44 + 15x + -1x2 = 0

Solving
44 + 15x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-44 + -15x + x2 = 0

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -15x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -15x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -15x + x2 = 0 + 44
-15x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-15x + x2 = 44

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 = 44 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 44 + 56.25

Combine like terms: 44 + 56.25 = 100.25
56.25 + -15x + x2 = 100.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + -7.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
x + -7.5 = 10.012492197

Simplifying
x + -7.5 = 10.012492197

Reorder the terms:
-7.5 + x = 10.012492197

Solving
-7.5 + x = 10.012492197

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 = 10.012492197 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 10.012492197 + 7.5
x = 10.012492197 + 7.5

Combine like terms: 10.012492197 + 7.5 = 17.512492197
x = 17.512492197

Simplifying
x = 17.512492197


Subproblem 2
x + -7.5 = -10.012492197

Simplifying
x + -7.5 = -10.012492197

Reorder the terms:
-7.5 + x = -10.012492197

Solving
-7.5 + x = -10.012492197

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 = -10.012492197 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -10.012492197 + 7.5
x = -10.012492197 + 7.5

Combine like terms: -10.012492197 + 7.5 = -2.512492197
x = -2.512492197

Simplifying
x = -2.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.512492197, -2.512492197}

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