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Simplifying 400 = 5t2 + 10t Reorder the terms: 400 = 10t + 5t2 Solving 400 = 10t + 5t2 Solving for variable 't'. Reorder the terms: 400 + -10t + -5t2 = 10t + -10t + 5t2 + -5t2 Combine like terms: 10t + -10t = 0 400 + -10t + -5t2 = 0 + 5t2 + -5t2 400 + -10t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 400 + -10t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(80 + -2t + -1t2) = 0 Factor a trinomial. 5((8 + -1t)(10 + t)) = 0 Ignore the factor 5.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 '(10 + t)' equal to zero and attempt to solve: Simplifying 10 + t = 0 Solving 10 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + t = 0 + -10 t = 0 + -10 Combine like terms: 0 + -10 = -10 t = -10 Simplifying t = -10Solution
t = {8, -10}
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