103=-16t^2+80t+3

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Solution for 103=-16t^2+80t+3 equation:


Simplifying
103 = -16t2 + 80t + 3

Reorder the terms:
103 = 3 + 80t + -16t2

Solving
103 = 3 + 80t + -16t2

Solving for variable 't'.

Combine like terms: 103 + -3 = 100
100 + -80t + 16t2 = 3 + 80t + -16t2 + -3 + -80t + 16t2

Reorder the terms:
100 + -80t + 16t2 = 3 + -3 + 80t + -80t + -16t2 + 16t2

Combine like terms: 3 + -3 = 0
100 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2
100 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
100 + -80t + 16t2 = 0 + -16t2 + 16t2
100 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
100 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + -20t + 4t2) = 0

Factor a trinomial.
4((5 + -2t)(5 + -2t)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5

Subproblem 2

Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5

Solution

t = {2.5, 2.5}

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