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Simplifying 10 = 6t2 + 7t Reorder the terms: 10 = 7t + 6t2 Solving 10 = 7t + 6t2 Solving for variable 't'. Reorder the terms: 10 + -7t + -6t2 = 7t + -7t + 6t2 + -6t2 Combine like terms: 7t + -7t = 0 10 + -7t + -6t2 = 0 + 6t2 + -6t2 10 + -7t + -6t2 = 6t2 + -6t2 Combine like terms: 6t2 + -6t2 = 0 10 + -7t + -6t2 = 0 Factor a trinomial. (5 + -6t)(2 + t) = 0Subproblem 1
Set the factor '(5 + -6t)' equal to zero and attempt to solve: Simplifying 5 + -6t = 0 Solving 5 + -6t = 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 + -6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6t = 0 + -5 -6t = 0 + -5 Combine like terms: 0 + -5 = -5 -6t = -5 Divide each side by '-6'. t = 0.8333333333 Simplifying t = 0.8333333333Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {0.8333333333, -2}
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