0=-16t^2+34t-4

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Solution for 0=-16t^2+34t-4 equation:


Simplifying
0 = -16t2 + 34t + -4

Reorder the terms:
0 = -4 + 34t + -16t2

Solving
0 = -4 + 34t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 4 = 4
4 + -34t + 16t2 = -4 + 34t + -16t2 + 4 + -34t + 16t2

Reorder the terms:
4 + -34t + 16t2 = -4 + 4 + 34t + -34t + -16t2 + 16t2

Combine like terms: -4 + 4 = 0
4 + -34t + 16t2 = 0 + 34t + -34t + -16t2 + 16t2
4 + -34t + 16t2 = 34t + -34t + -16t2 + 16t2

Combine like terms: 34t + -34t = 0
4 + -34t + 16t2 = 0 + -16t2 + 16t2
4 + -34t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
4 + -34t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -17t + 8t2) = 0

Factor a trinomial.
2((1 + -8t)(2 + -1t)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -8t)' equal to zero and attempt to solve: Simplifying 1 + -8t = 0 Solving 1 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8t = 0 + -1 -8t = 0 + -1 Combine like terms: 0 + -1 = -1 -8t = -1 Divide each side by '-8'. t = 0.125 Simplifying t = 0.125

Subproblem 2

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Solution

t = {0.125, 2}

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