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Simplifying t2 + 6t = 40 Reorder the terms: 6t + t2 = 40 Solving 6t + t2 = 40 Solving for variable 't'. Reorder the terms: -40 + 6t + t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 6t + t2 = 0 Factor a trinomial. (-10 + -1t)(4 + -1t) = 0Subproblem 1
Set the factor '(-10 + -1t)' equal to zero and attempt to solve: Simplifying -10 + -1t = 0 Solving -10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1t = 0 + 10 -1t = 0 + 10 Combine like terms: 0 + 10 = 10 -1t = 10 Divide each side by '-1'. t = -10 Simplifying t = -10Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-10, 4}
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