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Simplifying 16t2 + -800t + 6400 = 0 Reorder the terms: 6400 + -800t + 16t2 = 0 Solving 6400 + -800t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(400 + -50t + t2) = 0 Factor a trinomial. 16((10 + -1t)(40 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Subproblem 2
Set the factor '(40 + -1t)' equal to zero and attempt to solve: Simplifying 40 + -1t = 0 Solving 40 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1t = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1t = 0 + -40 -1t = 0 + -40 Combine like terms: 0 + -40 = -40 -1t = -40 Divide each side by '-1'. t = 40 Simplifying t = 40Solution
t = {10, 40}
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