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Simplifying 64 = -16t2 + 48t + 64 Reorder the terms: 64 = 64 + 48t + -16t2 Add '-64' to each side of the equation. 64 + -64 = 64 + 48t + -64 + -16t2 Combine like terms: 64 + -64 = 0 0 = 64 + 48t + -64 + -16t2 Reorder the terms: 0 = 64 + -64 + 48t + -16t2 Combine like terms: 64 + -64 = 0 0 = 0 + 48t + -16t2 0 = 48t + -16t2 Solving 0 = 48t + -16t2 Solving for variable 't'. Remove the zero: -48t + 16t2 = 48t + -16t2 + -48t + 16t2 Reorder the terms: -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -48t + 16t2 = 0 + -16t2 + 16t2 -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(-3 + t) = 0 Ignore the factor 16.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 '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Solution
t = {0, 3}
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