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Simplifying 10 = 16t2 + 70t + 10 Reorder the terms: 10 = 10 + 70t + 16t2 Add '-10' to each side of the equation. 10 + -10 = 10 + 70t + -10 + 16t2 Combine like terms: 10 + -10 = 0 0 = 10 + 70t + -10 + 16t2 Reorder the terms: 0 = 10 + -10 + 70t + 16t2 Combine like terms: 10 + -10 = 0 0 = 0 + 70t + 16t2 0 = 70t + 16t2 Solving 0 = 70t + 16t2 Solving for variable 't'. Remove the zero: -70t + -16t2 = 70t + 16t2 + -70t + -16t2 Reorder the terms: -70t + -16t2 = 70t + -70t + 16t2 + -16t2 Combine like terms: 70t + -70t = 0 -70t + -16t2 = 0 + 16t2 + -16t2 -70t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -70t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2t'. -2t(35 + 8t) = 0 Ignore the factor -2.Subproblem 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 '(35 + 8t)' equal to zero and attempt to solve: Simplifying 35 + 8t = 0 Solving 35 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + 8t = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 8t = 0 + -35 8t = 0 + -35 Combine like terms: 0 + -35 = -35 8t = -35 Divide each side by '8'. t = -4.375 Simplifying t = -4.375Solution
t = {0, -4.375}
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