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Simplifying 0 = 4t2 + -56t + 160 Reorder the terms: 0 = 160 + -56t + 4t2 Solving 0 = 160 + -56t + 4t2 Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + 56t + -4t2 = 160 + -56t + 4t2 + -160 + 56t + -4t2 Reorder the terms: -160 + 56t + -4t2 = 160 + -160 + -56t + 56t + 4t2 + -4t2 Combine like terms: 160 + -160 = 0 -160 + 56t + -4t2 = 0 + -56t + 56t + 4t2 + -4t2 -160 + 56t + -4t2 = -56t + 56t + 4t2 + -4t2 Combine like terms: -56t + 56t = 0 -160 + 56t + -4t2 = 0 + 4t2 + -4t2 -160 + 56t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -160 + 56t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 14t + -1t2) = 0 Factor a trinomial. 4((-10 + t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + t)' equal to zero and attempt to solve: Simplifying -10 + t = 0 Solving -10 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + t = 0 + 10 t = 0 + 10 Combine like terms: 0 + 10 = 10 t = 10 Simplifying t = 10Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {10, 4}
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