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Simplifying 10 = -16t2 + 36t + 10 Reorder the terms: 10 = 10 + 36t + -16t2 Add '-10' to each side of the equation. 10 + -10 = 10 + 36t + -10 + -16t2 Combine like terms: 10 + -10 = 0 0 = 10 + 36t + -10 + -16t2 Reorder the terms: 0 = 10 + -10 + 36t + -16t2 Combine like terms: 10 + -10 = 0 0 = 0 + 36t + -16t2 0 = 36t + -16t2 Solving 0 = 36t + -16t2 Solving for variable 't'. Remove the zero: -36t + 16t2 = 36t + -16t2 + -36t + 16t2 Reorder the terms: -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 -36t + 16t2 = 0 + -16t2 + 16t2 -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-9 + 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 '(-9 + 4t)' equal to zero and attempt to solve: Simplifying -9 + 4t = 0 Solving -9 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4t = 0 + 9 4t = 0 + 9 Combine like terms: 0 + 9 = 9 4t = 9 Divide each side by '4'. t = 2.25 Simplifying t = 2.25Solution
t = {0, 2.25}
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