400=-4.905(x^2)+20x

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Solution for 400=-4.905(x^2)+20x equation:


Simplifying
400 = -4.905(x2) + 20x

Reorder the terms:
400 = 20x + -4.905x2

Solving
400 = 20x + -4.905x2

Solving for variable 'x'.

Reorder the terms:
400 + -20x + 4.905x2 = 20x + -20x + -4.905x2 + 4.905x2

Combine like terms: 20x + -20x = 0
400 + -20x + 4.905x2 = 0 + -4.905x2 + 4.905x2
400 + -20x + 4.905x2 = -4.905x2 + 4.905x2

Combine like terms: -4.905x2 + 4.905x2 = 0.000
400 + -20x + 4.905x2 = 0.000

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

Divide each side by '4.905'.
81.54943935 + -4.077471967x + x2 = 0

Move the constant term to the right:

Add '-81.54943935' to each side of the equation.
81.54943935 + -4.077471967x + -81.54943935 + x2 = 0 + -81.54943935

Reorder the terms:
81.54943935 + -81.54943935 + -4.077471967x + x2 = 0 + -81.54943935

Combine like terms: 81.54943935 + -81.54943935 = 0.00000000
0.00000000 + -4.077471967x + x2 = 0 + -81.54943935
-4.077471967x + x2 = 0 + -81.54943935

Combine like terms: 0 + -81.54943935 = -81.54943935
-4.077471967x + x2 = -81.54943935

The x term is -4.077471967x.  Take half its coefficient (-2.038735984).
Square it (4.156444412) and add it to both sides.

Add '4.156444412' to each side of the equation.
-4.077471967x + 4.156444412 + x2 = -81.54943935 + 4.156444412

Reorder the terms:
4.156444412 + -4.077471967x + x2 = -81.54943935 + 4.156444412

Combine like terms: -81.54943935 + 4.156444412 = -77.392994938
4.156444412 + -4.077471967x + x2 = -77.392994938

Factor a perfect square on the left side:
(x + -2.038735984)(x + -2.038735984) = -77.392994938

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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