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Simplifying 52 = -16t2 + 12t + 52 Reorder the terms: 52 = 52 + 12t + -16t2 Add '-52' to each side of the equation. 52 + -52 = 52 + 12t + -52 + -16t2 Combine like terms: 52 + -52 = 0 0 = 52 + 12t + -52 + -16t2 Reorder the terms: 0 = 52 + -52 + 12t + -16t2 Combine like terms: 52 + -52 = 0 0 = 0 + 12t + -16t2 0 = 12t + -16t2 Solving 0 = 12t + -16t2 Solving for variable 't'. Remove the zero: -12t + 16t2 = 12t + -16t2 + -12t + 16t2 Reorder the terms: -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -12t + 16t2 = 0 + -16t2 + 16t2 -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-3 + 4t) = 0 Ignore the factor 4.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 + 4t)' equal to zero and attempt to solve: Simplifying -3 + 4t = 0 Solving -3 + 4t = 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 + 4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4t = 0 + 3 4t = 0 + 3 Combine like terms: 0 + 3 = 3 4t = 3 Divide each side by '4'. t = 0.75 Simplifying t = 0.75Solution
t = {0, 0.75}
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