50+t^2=16t-5

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Solution for 50+t^2=16t-5 equation:


Simplifying
50 + t2 = 16t + -5

Reorder the terms:
50 + t2 = -5 + 16t

Solving
50 + t2 = -5 + 16t

Solving for variable 't'.

Reorder the terms:
50 + 5 + -16t + t2 = -5 + 16t + 5 + -16t

Combine like terms: 50 + 5 = 55
55 + -16t + t2 = -5 + 16t + 5 + -16t

Reorder the terms:
55 + -16t + t2 = -5 + 5 + 16t + -16t

Combine like terms: -5 + 5 = 0
55 + -16t + t2 = 0 + 16t + -16t
55 + -16t + t2 = 16t + -16t

Combine like terms: 16t + -16t = 0
55 + -16t + t2 = 0

Factor a trinomial.
(5 + -1t)(11 + -1t) = 0

Subproblem 1

Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5

Subproblem 2

Set the factor '(11 + -1t)' equal to zero and attempt to solve: Simplifying 11 + -1t = 0 Solving 11 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1t = 0 + -11 -1t = 0 + -11 Combine like terms: 0 + -11 = -11 -1t = -11 Divide each side by '-1'. t = 11 Simplifying t = 11

Solution

t = {5, 11}

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