20x-x^2=120

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Solution for 20x-x^2=120 equation:


Simplifying
20x + -1x2 = 120

Solving
20x + -1x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 20x + -1x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 20x + -1x2 = 0

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

Divide each side by '-1'.
120 + -20x + x2 = 0

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -20x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -20x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -20x + x2 = 0 + -120
-20x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-20x + x2 = -120

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -120 + 100

Reorder the terms:
100 + -20x + x2 = -120 + 100

Combine like terms: -120 + 100 = -20
100 + -20x + x2 = -20

Factor a perfect square on the left side:
(x + -10)(x + -10) = -20

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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