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Simplifying 18t2 + 12t = 70 Reorder the terms: 12t + 18t2 = 70 Solving 12t + 18t2 = 70 Solving for variable 't'. Reorder the terms: -70 + 12t + 18t2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 12t + 18t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 6t + 9t2) = 0 Factor a trinomial. 2((-7 + -3t)(5 + -3t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3t)' equal to zero and attempt to solve: Simplifying -7 + -3t = 0 Solving -7 + -3t = 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 + -3t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3t = 0 + 7 -3t = 0 + 7 Combine like terms: 0 + 7 = 7 -3t = 7 Divide each side by '-3'. t = -2.333333333 Simplifying t = -2.333333333Subproblem 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 = {-2.333333333, 1.666666667}
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