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Simplifying 292 = 4t2 + -53t + 187 Reorder the terms: 292 = 187 + -53t + 4t2 Solving 292 = 187 + -53t + 4t2 Solving for variable 't'. Combine like terms: 292 + -187 = 105 105 + 53t + -4t2 = 187 + -53t + 4t2 + -187 + 53t + -4t2 Reorder the terms: 105 + 53t + -4t2 = 187 + -187 + -53t + 53t + 4t2 + -4t2 Combine like terms: 187 + -187 = 0 105 + 53t + -4t2 = 0 + -53t + 53t + 4t2 + -4t2 105 + 53t + -4t2 = -53t + 53t + 4t2 + -4t2 Combine like terms: -53t + 53t = 0 105 + 53t + -4t2 = 0 + 4t2 + -4t2 105 + 53t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 105 + 53t + -4t2 = 0 Factor a trinomial. (15 + -1t)(7 + 4t) = 0Subproblem 1
Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15Subproblem 2
Set the factor '(7 + 4t)' equal to zero and attempt to solve: Simplifying 7 + 4t = 0 Solving 7 + 4t = 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 + 4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4t = 0 + -7 4t = 0 + -7 Combine like terms: 0 + -7 = -7 4t = -7 Divide each side by '4'. t = -1.75 Simplifying t = -1.75Solution
t = {15, -1.75}
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