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Simplifying 585 = 5t2 + 20t Reorder the terms: 585 = 20t + 5t2 Solving 585 = 20t + 5t2 Solving for variable 't'. Reorder the terms: 585 + -20t + -5t2 = 20t + -20t + 5t2 + -5t2 Combine like terms: 20t + -20t = 0 585 + -20t + -5t2 = 0 + 5t2 + -5t2 585 + -20t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 585 + -20t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(117 + -4t + -1t2) = 0 Factor a trinomial. 5((9 + -1t)(13 + t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Subproblem 2
Set the factor '(13 + t)' equal to zero and attempt to solve: Simplifying 13 + t = 0 Solving 13 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + t = 0 + -13 t = 0 + -13 Combine like terms: 0 + -13 = -13 t = -13 Simplifying t = -13Solution
t = {9, -13}
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