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Simplifying 10 = -16t2 + 27t + 10 Reorder the terms: 10 = 10 + 27t + -16t2 Add '-10' to each side of the equation. 10 + -10 = 10 + 27t + -10 + -16t2 Combine like terms: 10 + -10 = 0 0 = 10 + 27t + -10 + -16t2 Reorder the terms: 0 = 10 + -10 + 27t + -16t2 Combine like terms: 10 + -10 = 0 0 = 0 + 27t + -16t2 0 = 27t + -16t2 Solving 0 = 27t + -16t2 Solving for variable 't'. Remove the zero: -27t + 16t2 = 27t + -16t2 + -27t + 16t2 Reorder the terms: -27t + 16t2 = 27t + -27t + -16t2 + 16t2 Combine like terms: 27t + -27t = 0 -27t + 16t2 = 0 + -16t2 + 16t2 -27t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -27t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-27 + 16t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-27 + 16t)' equal to zero and attempt to solve: Simplifying -27 + 16t = 0 Solving -27 + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 16t = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 16t = 0 + 27 16t = 0 + 27 Combine like terms: 0 + 27 = 27 16t = 27 Divide each side by '16'. t = 1.6875 Simplifying t = 1.6875Solution
t = {0, 1.6875}
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