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Simplifying -15t2 + 135t + 10 = 220 Reorder the terms: 10 + 135t + -15t2 = 220 Solving 10 + 135t + -15t2 = 220 Solving for variable 't'. Reorder the terms: 10 + -220 + 135t + -15t2 = 220 + -220 Combine like terms: 10 + -220 = -210 -210 + 135t + -15t2 = 220 + -220 Combine like terms: 220 + -220 = 0 -210 + 135t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-14 + 9t + -1t2) = 0 Factor a trinomial. 15((-7 + t)(2 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 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 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {7, 2}
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