-x^2+10x+16=0

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Solution for -x^2+10x+16=0 equation: 


Simplifying
-1x2 + 10x + 16 = 0

Reorder the terms:
16 + 10x + -1x2 = 0

Solving
16 + 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'.
-16 + -10x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -10x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10x + x2 = 0 + 16
-10x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-10x + x2 = 16

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 = 16 + 25

Reorder the terms:
25 + -10x + x2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10x + x2 = 41

Factor a perfect square on the left side:
(x + -5)(x + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -5 = 6.403124237

Simplifying
x + -5 = 6.403124237

Reorder the terms:
-5 + x = 6.403124237

Solving
-5 + x = 6.403124237

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 = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.403124237 + 5
x = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
x = 11.403124237

Simplifying
x = 11.403124237


Subproblem 2
x + -5 = -6.403124237

Simplifying
x + -5 = -6.403124237

Reorder the terms:
-5 + x = -6.403124237

Solving
-5 + x = -6.403124237

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 = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.403124237 + 5
x = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
x = -1.403124237

Simplifying
x = -1.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.403124237, -1.403124237}

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