t^2=45-4t

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Solution for t^2=45-4t equation:


Simplifying
t2 = 45 + -4t

Solving
t2 = 45 + -4t

Solving for variable 't'.

Reorder the terms:
-45 + 4t + t2 = 45 + -4t + -45 + 4t

Reorder the terms:
-45 + 4t + t2 = 45 + -45 + -4t + 4t

Combine like terms: 45 + -45 = 0
-45 + 4t + t2 = 0 + -4t + 4t
-45 + 4t + t2 = -4t + 4t

Combine like terms: -4t + 4t = 0
-45 + 4t + t2 = 0

Factor a trinomial.
(-9 + -1t)(5 + -1t) = 0

Subproblem 1

Set the factor '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9

Subproblem 2

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

Solution

t = {-9, 5}

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