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Simplifying 400 = -16t2 + 164t Reorder the terms: 400 = 164t + -16t2 Solving 400 = 164t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -164t + 16t2 = 164t + -164t + -16t2 + 16t2 Combine like terms: 164t + -164t = 0 400 + -164t + 16t2 = 0 + -16t2 + 16t2 400 + -164t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -164t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -41t + 4t2) = 0 Factor a trinomial. 4((4 + -1t)(25 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(25 + -4t)' equal to zero and attempt to solve: Simplifying 25 + -4t = 0 Solving 25 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -4t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -4t = 0 + -25 -4t = 0 + -25 Combine like terms: 0 + -25 = -25 -4t = -25 Divide each side by '-4'. t = 6.25 Simplifying t = 6.25Solution
t = {4, 6.25}
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