t=-0.8t^2+40t-250

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Solution for t=-0.8t^2+40t-250 equation:


Simplifying
t = -0.8t2 + 40t + -250

Reorder the terms:
t = -250 + 40t + -0.8t2

Solving
t = -250 + 40t + -0.8t2

Solving for variable 't'.

Reorder the terms:
250 + t + -40t + 0.8t2 = -250 + 40t + -0.8t2 + 250 + -40t + 0.8t2

Combine like terms: t + -40t = -39t
250 + -39t + 0.8t2 = -250 + 40t + -0.8t2 + 250 + -40t + 0.8t2

Reorder the terms:
250 + -39t + 0.8t2 = -250 + 250 + 40t + -40t + -0.8t2 + 0.8t2

Combine like terms: -250 + 250 = 0
250 + -39t + 0.8t2 = 0 + 40t + -40t + -0.8t2 + 0.8t2
250 + -39t + 0.8t2 = 40t + -40t + -0.8t2 + 0.8t2

Combine like terms: 40t + -40t = 0
250 + -39t + 0.8t2 = 0 + -0.8t2 + 0.8t2
250 + -39t + 0.8t2 = -0.8t2 + 0.8t2

Combine like terms: -0.8t2 + 0.8t2 = 0.0
250 + -39t + 0.8t2 = 0.0

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

Divide each side by '0.8'.
312.5 + -48.75t + t2 = 0

Move the constant term to the right:

Add '-312.5' to each side of the equation.
312.5 + -48.75t + -312.5 + t2 = 0 + -312.5

Reorder the terms:
312.5 + -312.5 + -48.75t + t2 = 0 + -312.5

Combine like terms: 312.5 + -312.5 = 0.0
0.0 + -48.75t + t2 = 0 + -312.5
-48.75t + t2 = 0 + -312.5

Combine like terms: 0 + -312.5 = -312.5
-48.75t + t2 = -312.5

The t term is -48.75t.  Take half its coefficient (-24.375).
Square it (594.140625) and add it to both sides.

Add '594.140625' to each side of the equation.
-48.75t + 594.140625 + t2 = -312.5 + 594.140625

Reorder the terms:
594.140625 + -48.75t + t2 = -312.5 + 594.140625

Combine like terms: -312.5 + 594.140625 = 281.640625
594.140625 + -48.75t + t2 = 281.640625

Factor a perfect square on the left side:
(t + -24.375)(t + -24.375) = 281.640625

Calculate the square root of the right side: 16.782151978

Break this problem into two subproblems by setting 
(t + -24.375) equal to 16.782151978 and -16.782151978.

Subproblem 1

t + -24.375 = 16.782151978 Simplifying t + -24.375 = 16.782151978 Reorder the terms: -24.375 + t = 16.782151978 Solving -24.375 + t = 16.782151978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24.375' to each side of the equation. -24.375 + 24.375 + t = 16.782151978 + 24.375 Combine like terms: -24.375 + 24.375 = 0.000 0.000 + t = 16.782151978 + 24.375 t = 16.782151978 + 24.375 Combine like terms: 16.782151978 + 24.375 = 41.157151978 t = 41.157151978 Simplifying t = 41.157151978

Subproblem 2

t + -24.375 = -16.782151978 Simplifying t + -24.375 = -16.782151978 Reorder the terms: -24.375 + t = -16.782151978 Solving -24.375 + t = -16.782151978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24.375' to each side of the equation. -24.375 + 24.375 + t = -16.782151978 + 24.375 Combine like terms: -24.375 + 24.375 = 0.000 0.000 + t = -16.782151978 + 24.375 t = -16.782151978 + 24.375 Combine like terms: -16.782151978 + 24.375 = 7.592848022 t = 7.592848022 Simplifying t = 7.592848022

Solution

The solution to the problem is based on the solutions from the subproblems. t = {41.157151978, 7.592848022}

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