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Simplifying 4t2 = 25t + 21 Reorder the terms: 4t2 = 21 + 25t Solving 4t2 = 21 + 25t Solving for variable 't'. Reorder the terms: -21 + -25t + 4t2 = 21 + 25t + -21 + -25t Reorder the terms: -21 + -25t + 4t2 = 21 + -21 + 25t + -25t Combine like terms: 21 + -21 = 0 -21 + -25t + 4t2 = 0 + 25t + -25t -21 + -25t + 4t2 = 25t + -25t Combine like terms: 25t + -25t = 0 -21 + -25t + 4t2 = 0 Factor a trinomial. (-3 + -4t)(7 + -1t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-0.75, 7}
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