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Simplifying -46 = t(9 + (-16t)) -46 = (9 * t + (-16t) * t) -46 = (9t + -16t2) Solving -46 = 9t + -16t2 Solving for variable 't'. Reorder the terms: -46 + -9t + 16t2 = 9t + -9t + -16t2 + 16t2 Combine like terms: 9t + -9t = 0 -46 + -9t + 16t2 = 0 + -16t2 + 16t2 -46 + -9t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -46 + -9t + 16t2 = 0 Factor a trinomial. (-23 + -16t)(2 + -1t) = 0Subproblem 1
Set the factor '(-23 + -16t)' equal to zero and attempt to solve: Simplifying -23 + -16t = 0 Solving -23 + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -16t = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -16t = 0 + 23 -16t = 0 + 23 Combine like terms: 0 + 23 = 23 -16t = 23 Divide each side by '-16'. t = -1.4375 Simplifying t = -1.4375Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-1.4375, 2}
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