2x-x^2=12

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Solution for 2x-x^2=12 equation:


Simplifying
2x + -1x2 = 12

Solving
2x + -1x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 2x + -1x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 2x + -1x2 = 0

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

Divide each side by '-1'.
12 + -2x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -2x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -2x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -2x + x2 = 0 + -12
-2x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-2x + x2 = -12

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 = -12 + 1

Reorder the terms:
1 + -2x + x2 = -12 + 1

Combine like terms: -12 + 1 = -11
1 + -2x + x2 = -11

Factor a perfect square on the left side:
(x + -1)(x + -1) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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