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Simplifying 225t2 + -200t + 70 = 40t + 6 Reorder the terms: 70 + -200t + 225t2 = 40t + 6 Reorder the terms: 70 + -200t + 225t2 = 6 + 40t Solving 70 + -200t + 225t2 = 6 + 40t Solving for variable 't'. Reorder the terms: 70 + -6 + -200t + -40t + 225t2 = 6 + 40t + -6 + -40t Combine like terms: 70 + -6 = 64 64 + -200t + -40t + 225t2 = 6 + 40t + -6 + -40t Combine like terms: -200t + -40t = -240t 64 + -240t + 225t2 = 6 + 40t + -6 + -40t Reorder the terms: 64 + -240t + 225t2 = 6 + -6 + 40t + -40t Combine like terms: 6 + -6 = 0 64 + -240t + 225t2 = 0 + 40t + -40t 64 + -240t + 225t2 = 40t + -40t Combine like terms: 40t + -40t = 0 64 + -240t + 225t2 = 0 Factor a trinomial. (8 + -15t)(8 + -15t) = 0Subproblem 1
Set the factor '(8 + -15t)' equal to zero and attempt to solve: Simplifying 8 + -15t = 0 Solving 8 + -15t = 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 + -15t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -15t = 0 + -8 -15t = 0 + -8 Combine like terms: 0 + -8 = -8 -15t = -8 Divide each side by '-15'. t = 0.5333333333 Simplifying t = 0.5333333333Subproblem 2
Set the factor '(8 + -15t)' equal to zero and attempt to solve: Simplifying 8 + -15t = 0 Solving 8 + -15t = 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 + -15t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -15t = 0 + -8 -15t = 0 + -8 Combine like terms: 0 + -8 = -8 -15t = -8 Divide each side by '-15'. t = 0.5333333333 Simplifying t = 0.5333333333Solution
t = {0.5333333333, 0.5333333333}
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