8.3=-1.5t^2+25t

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Solution for 8.3=-1.5t^2+25t equation: 


Simplifying
8.3 = -1.5t2 + 25t

Reorder the terms:
8.3 = 25t + -1.5t2

Solving
8.3 = 25t + -1.5t2

Solving for variable 't'.

Reorder the terms:
8.3 + -25t + 1.5t2 = 25t + -25t + -1.5t2 + 1.5t2

Combine like terms: 25t + -25t = 0
8.3 + -25t + 1.5t2 = 0 + -1.5t2 + 1.5t2
8.3 + -25t + 1.5t2 = -1.5t2 + 1.5t2

Combine like terms: -1.5t2 + 1.5t2 = 0.0
8.3 + -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'.
5.533333333 + -16.66666667t + t2 = 0

Move the constant term to the right:

Add '-5.533333333' to each side of the equation.
5.533333333 + -16.66666667t + -5.533333333 + t2 = 0 + -5.533333333

Reorder the terms:
5.533333333 + -5.533333333 + -16.66666667t + t2 = 0 + -5.533333333

Combine like terms: 5.533333333 + -5.533333333 = 0.000000000
0.000000000 + -16.66666667t + t2 = 0 + -5.533333333
-16.66666667t + t2 = 0 + -5.533333333

Combine like terms: 0 + -5.533333333 = -5.533333333
-16.66666667t + t2 = -5.533333333

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 = -5.533333333 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667t + t2 = -5.533333333 + 69.44444447

Combine like terms: -5.533333333 + 69.44444447 = 63.911111137
69.44444447 + -16.66666667t + t2 = 63.911111137

Factor a perfect square on the left side:
(t + -8.333333335)(t + -8.333333335) = 63.911111137

Calculate the square root of the right side: 7.994442516

Break this problem into two subproblems by setting 
(t + -8.333333335) equal to 7.994442516 and -7.994442516.


Subproblem 1
t + -8.333333335 = 7.994442516

Simplifying
t + -8.333333335 = 7.994442516

Reorder the terms:
-8.333333335 + t = 7.994442516

Solving
-8.333333335 + t = 7.994442516

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 = 7.994442516 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = 7.994442516 + 8.333333335
t = 7.994442516 + 8.333333335

Combine like terms: 7.994442516 + 8.333333335 = 16.327775851
t = 16.327775851

Simplifying
t = 16.327775851


Subproblem 2
t + -8.333333335 = -7.994442516

Simplifying
t + -8.333333335 = -7.994442516

Reorder the terms:
-8.333333335 + t = -7.994442516

Solving
-8.333333335 + t = -7.994442516

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 = -7.994442516 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + t = -7.994442516 + 8.333333335
t = -7.994442516 + 8.333333335

Combine like terms: -7.994442516 + 8.333333335 = 0.338890819
t = 0.338890819

Simplifying
t = 0.338890819


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.327775851, 0.338890819}

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