-x^2+8x+44=0

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Solution for -x^2+8x+44=0 equation: 


Simplifying
-1x2 + 8x + 44 = 0

Reorder the terms:
44 + 8x + -1x2 = 0

Solving
44 + 8x + -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 + -8x + x2 = 0

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -8x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -8x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -8x + x2 = 0 + 44
-8x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-8x + x2 = 44

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 44 + 16

Reorder the terms:
16 + -8x + x2 = 44 + 16

Combine like terms: 44 + 16 = 60
16 + -8x + x2 = 60

Factor a perfect square on the left side:
(x + -4)(x + -4) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + -4) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + -4 = 7.745966692

Simplifying
x + -4 = 7.745966692

Reorder the terms:
-4 + x = 7.745966692

Solving
-4 + x = 7.745966692

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 7.745966692 + 4

Combine like terms: -4 + 4 = 0
0 + x = 7.745966692 + 4
x = 7.745966692 + 4

Combine like terms: 7.745966692 + 4 = 11.745966692
x = 11.745966692

Simplifying
x = 11.745966692


Subproblem 2
x + -4 = -7.745966692

Simplifying
x + -4 = -7.745966692

Reorder the terms:
-4 + x = -7.745966692

Solving
-4 + x = -7.745966692

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -7.745966692 + 4

Combine like terms: -4 + 4 = 0
0 + x = -7.745966692 + 4
x = -7.745966692 + 4

Combine like terms: -7.745966692 + 4 = -3.745966692
x = -3.745966692

Simplifying
x = -3.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.745966692, -3.745966692}

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