50=-1.5t^2+25t

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Solution for 50=-1.5t^2+25t equation: 


Simplifying
50 = -1.5t2 + 25t

Reorder the terms:
50 = 25t + -1.5t2

Solving
50 = 25t + -1.5t2

Solving for variable 't'.

Reorder the terms:
50 + -25t + 1.5t2 = 25t + -25t + -1.5t2 + 1.5t2

Combine like terms: 25t + -25t = 0
50 + -25t + 1.5t2 = 0 + -1.5t2 + 1.5t2
50 + -25t + 1.5t2 = -1.5t2 + 1.5t2

Combine like terms: -1.5t2 + 1.5t2 = 0.0
50 + -25t + 1.5t2 = 0.0

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

Divide each side by '1.5'.
33.33333333 + -16.66666667t + t2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -16.66666667t + -33.33333333 + t2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -16.66666667t + t2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -16.66666667t + t2 = 0 + -33.33333333
-16.66666667t + t2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-16.66666667t + t2 = -33.33333333

The t term is -16.66666667t.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667t + 69.44444447 + t2 = -33.33333333 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667t + t2 = -33.33333333 + 69.44444447

Combine like terms: -33.33333333 + 69.44444447 = 36.11111114
69.44444447 + -16.66666667t + t2 = 36.11111114

Factor a perfect square on the left side:
(t + -8.333333335)(t + -8.333333335) = 36.11111114

Calculate the square root of the right side: 6.009252128

Break this problem into two subproblems by setting 
(t + -8.333333335) equal to 6.009252128 and -6.009252128.


Subproblem 1
t + -8.333333335 = 6.009252128

Simplifying
t + -8.333333335 = 6.009252128

Reorder the terms:
-8.333333335 + t = 6.009252128

Solving
-8.333333335 + t = 6.009252128

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = 6.009252128 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = 6.009252128 + 8.333333335
t = 6.009252128 + 8.333333335

Combine like terms: 6.009252128 + 8.333333335 = 14.342585463
t = 14.342585463

Simplifying
t = 14.342585463


Subproblem 2
t + -8.333333335 = -6.009252128

Simplifying
t + -8.333333335 = -6.009252128

Reorder the terms:
-8.333333335 + t = -6.009252128

Solving
-8.333333335 + t = -6.009252128

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + t = -6.009252128 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = -6.009252128 + 8.333333335
t = -6.009252128 + 8.333333335

Combine like terms: -6.009252128 + 8.333333335 = 2.324081207
t = 2.324081207

Simplifying
t = 2.324081207


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.342585463, 2.324081207}

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