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Simplifying 43 = -16t2 + 186t + 43 Reorder the terms: 43 = 43 + 186t + -16t2 Add '-43' to each side of the equation. 43 + -43 = 43 + 186t + -43 + -16t2 Combine like terms: 43 + -43 = 0 0 = 43 + 186t + -43 + -16t2 Reorder the terms: 0 = 43 + -43 + 186t + -16t2 Combine like terms: 43 + -43 = 0 0 = 0 + 186t + -16t2 0 = 186t + -16t2 Solving 0 = 186t + -16t2 Solving for variable 't'. Remove the zero: -186t + 16t2 = 186t + -16t2 + -186t + 16t2 Reorder the terms: -186t + 16t2 = 186t + -186t + -16t2 + 16t2 Combine like terms: 186t + -186t = 0 -186t + 16t2 = 0 + -16t2 + 16t2 -186t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -186t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-93 + 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 '(-93 + 8t)' equal to zero and attempt to solve: Simplifying -93 + 8t = 0 Solving -93 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '93' to each side of the equation. -93 + 93 + 8t = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 8t = 0 + 93 8t = 0 + 93 Combine like terms: 0 + 93 = 93 8t = 93 Divide each side by '8'. t = 11.625 Simplifying t = 11.625Solution
t = {0, 11.625}
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