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Simplifying 30t2 + 8 = 35t + 8 Reorder the terms: 8 + 30t2 = 35t + 8 Reorder the terms: 8 + 30t2 = 8 + 35t Add '-8' to each side of the equation. 8 + -8 + 30t2 = 8 + -8 + 35t Combine like terms: 8 + -8 = 0 0 + 30t2 = 8 + -8 + 35t 30t2 = 8 + -8 + 35t Combine like terms: 8 + -8 = 0 30t2 = 0 + 35t 30t2 = 35t Solving 30t2 = 35t Solving for variable 't'. Reorder the terms: -35t + 30t2 = 35t + -35t Combine like terms: 35t + -35t = 0 -35t + 30t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(-7 + 6t) = 0 Ignore the factor 5.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-7 + 6t)' equal to zero and attempt to solve: Simplifying -7 + 6t = 0 Solving -7 + 6t = 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 + 6t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 6t = 0 + 7 6t = 0 + 7 Combine like terms: 0 + 7 = 7 6t = 7 Divide each side by '6'. t = 1.166666667 Simplifying t = 1.166666667Solution
t = {0, 1.166666667}
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