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Simplifying (0.5) * 10t2 + 20t = 480 Multiply 0.5 * 10 5t2 + 20t = 480 Reorder the terms: 20t + 5t2 = 480 Solving 20t + 5t2 = 480 Solving for variable 't'. Reorder the terms: -480 + 20t + 5t2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 20t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-96 + 4t + t2) = 0 Factor a trinomial. 5((-12 + -1t)(8 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-12 + -1t)' equal to zero and attempt to solve: Simplifying -12 + -1t = 0 Solving -12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1t = 0 + 12 -1t = 0 + 12 Combine like terms: 0 + 12 = 12 -1t = 12 Divide each side by '-1'. t = -12 Simplifying t = -12Subproblem 2
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 = 8Solution
t = {-12, 8}
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