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Simplifying 520 = -16t2 + 108t + 520 Reorder the terms: 520 = 520 + 108t + -16t2 Add '-520' to each side of the equation. 520 + -520 = 520 + 108t + -520 + -16t2 Combine like terms: 520 + -520 = 0 0 = 520 + 108t + -520 + -16t2 Reorder the terms: 0 = 520 + -520 + 108t + -16t2 Combine like terms: 520 + -520 = 0 0 = 0 + 108t + -16t2 0 = 108t + -16t2 Solving 0 = 108t + -16t2 Solving for variable 't'. Remove the zero: -108t + 16t2 = 108t + -16t2 + -108t + 16t2 Reorder the terms: -108t + 16t2 = 108t + -108t + -16t2 + 16t2 Combine like terms: 108t + -108t = 0 -108t + 16t2 = 0 + -16t2 + 16t2 -108t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -108t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-27 + 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 '(-27 + 4t)' equal to zero and attempt to solve: Simplifying -27 + 4t = 0 Solving -27 + 4t = 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 + 4t = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4t = 0 + 27 4t = 0 + 27 Combine like terms: 0 + 27 = 27 4t = 27 Divide each side by '4'. t = 6.75 Simplifying t = 6.75Solution
t = {0, 6.75}
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