-x^2+10x+22=0

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Solution for -x^2+10x+22=0 equation: 


Simplifying
-1x2 + 10x + 22 = 0

Reorder the terms:
22 + 10x + -1x2 = 0

Solving
22 + 10x + -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'.
-22 + -10x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -10x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -10x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -10x + x2 = 0 + 22
-10x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-10x + x2 = 22

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 22 + 25

Reorder the terms:
25 + -10x + x2 = 22 + 25

Combine like terms: 22 + 25 = 47
25 + -10x + x2 = 47

Factor a perfect square on the left side:
(x + -5)(x + -5) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -5) equal to 6.8556546 and -6.8556546.


Subproblem 1
x + -5 = 6.8556546

Simplifying
x + -5 = 6.8556546

Reorder the terms:
-5 + x = 6.8556546

Solving
-5 + x = 6.8556546

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 6.8556546 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.8556546 + 5
x = 6.8556546 + 5

Combine like terms: 6.8556546 + 5 = 11.8556546
x = 11.8556546

Simplifying
x = 11.8556546


Subproblem 2
x + -5 = -6.8556546

Simplifying
x + -5 = -6.8556546

Reorder the terms:
-5 + x = -6.8556546

Solving
-5 + x = -6.8556546

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -6.8556546 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.8556546 + 5
x = -6.8556546 + 5

Combine like terms: -6.8556546 + 5 = -1.8556546
x = -1.8556546

Simplifying
x = -1.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.8556546, -1.8556546}

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