2x-x^2=16

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Solution for 2x-x^2=16 equation:


Simplifying
2x + -1x2 = 16

Solving
2x + -1x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 2x + -1x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 2x + -1x2 = 0

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

Divide each side by '-1'.
16 + -2x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -2x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -2x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -2x + x2 = 0 + -16
-2x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-2x + x2 = -16

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -16 + 1

Reorder the terms:
1 + -2x + x2 = -16 + 1

Combine like terms: -16 + 1 = -15
1 + -2x + x2 = -15

Factor a perfect square on the left side:
(x + -1)(x + -1) = -15

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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