100=20t-3t^2

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Solution for 100=20t-3t^2 equation: 


Simplifying
100 = 20t + -3t2

Solving
100 = 20t + -3t2

Solving for variable 't'.

Reorder the terms:
100 + -20t + 3t2 = 20t + -20t + -3t2 + 3t2

Combine like terms: 20t + -20t = 0
100 + -20t + 3t2 = 0 + -3t2 + 3t2
100 + -20t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
100 + -20t + 3t2 = 0

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

Divide each side by '3'.
33.33333333 + -6.666666667t + t2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -6.666666667t + -33.33333333 + t2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -6.666666667t + t2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -6.666666667t + t2 = 0 + -33.33333333
-6.666666667t + t2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-6.666666667t + t2 = -33.33333333

The t term is -6.666666667t.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667t + 11.11111112 + t2 = -33.33333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667t + t2 = -33.33333333 + 11.11111112

Combine like terms: -33.33333333 + 11.11111112 = -22.22222221
11.11111112 + -6.666666667t + t2 = -22.22222221

Factor a perfect square on the left side:
(t + -3.333333334)(t + -3.333333334) = -22.22222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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