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Simplifying 250t2 + 100t + 550 = 2500 Reorder the terms: 550 + 100t + 250t2 = 2500 Solving 550 + 100t + 250t2 = 2500 Solving for variable 't'. Reorder the terms: 550 + -2500 + 100t + 250t2 = 2500 + -2500 Combine like terms: 550 + -2500 = -1950 -1950 + 100t + 250t2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -1950 + 100t + 250t2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(-39 + 2t + 5t2) = 0 Factor a trinomial. 50((-3 + -1t)(13 + -5t)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 2
Set the factor '(13 + -5t)' equal to zero and attempt to solve: Simplifying 13 + -5t = 0 Solving 13 + -5t = 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 + -5t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -5t = 0 + -13 -5t = 0 + -13 Combine like terms: 0 + -13 = -13 -5t = -13 Divide each side by '-5'. t = 2.6 Simplifying t = 2.6Solution
t = {-3, 2.6}
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