2(x-2)-x^2=48

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Solution for 2(x-2)-x^2=48 equation:


Simplifying
2(x + -2) + -1x2 = 48

Reorder the terms:
2(-2 + x) + -1x2 = 48
(-2 * 2 + x * 2) + -1x2 = 48
(-4 + 2x) + -1x2 = 48

Solving
-4 + 2x + -1x2 = 48

Solving for variable 'x'.

Reorder the terms:
-4 + -48 + 2x + -1x2 = 48 + -48

Combine like terms: -4 + -48 = -52
-52 + 2x + -1x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-52 + 2x + -1x2 = 0

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

Divide each side by '-1'.
52 + -2x + x2 = 0

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + -2x + -52 + x2 = 0 + -52

Reorder the terms:
52 + -52 + -2x + x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -2x + x2 = 0 + -52
-2x + x2 = 0 + -52

Combine like terms: 0 + -52 = -52
-2x + x2 = -52

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 = -52 + 1

Reorder the terms:
1 + -2x + x2 = -52 + 1

Combine like terms: -52 + 1 = -51
1 + -2x + x2 = -51

Factor a perfect square on the left side:
(x + -1)(x + -1) = -51

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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