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Simplifying 400 = 4t2 + 18t Reorder the terms: 400 = 18t + 4t2 Solving 400 = 18t + 4t2 Solving for variable 't'. Reorder the terms: 400 + -18t + -4t2 = 18t + -18t + 4t2 + -4t2 Combine like terms: 18t + -18t = 0 400 + -18t + -4t2 = 0 + 4t2 + -4t2 400 + -18t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 400 + -18t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -9t + -2t2) = 0 Factor a trinomial. 2((8 + -1t)(25 + 2t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Subproblem 2
Set the factor '(25 + 2t)' equal to zero and attempt to solve: Simplifying 25 + 2t = 0 Solving 25 + 2t = 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 + 2t = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2t = 0 + -25 2t = 0 + -25 Combine like terms: 0 + -25 = -25 2t = -25 Divide each side by '2'. t = -12.5 Simplifying t = -12.5Solution
t = {8, -12.5}
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