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Simplifying 4t2 + 100 = 40t Reorder the terms: 100 + 4t2 = 40t Solving 100 + 4t2 = 40t Solving for variable 't'. Reorder the terms: 100 + -40t + 4t2 = 40t + -40t Combine like terms: 40t + -40t = 0 100 + -40t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -10t + t2) = 0 Factor a trinomial. 4((5 + -1t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {5, 5}
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