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Simplifying t(6t + 5) = 25 Reorder the terms: t(5 + 6t) = 25 (5 * t + 6t * t) = 25 (5t + 6t2) = 25 Solving 5t + 6t2 = 25 Solving for variable 't'. Reorder the terms: -25 + 5t + 6t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 5t + 6t2 = 0 Factor a trinomial. (-5 + -2t)(5 + -3t) = 0Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {-2.5, 1.666666667}
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