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Simplifying 4t(t + -1) = 224 Reorder the terms: 4t(-1 + t) = 224 (-1 * 4t + t * 4t) = 224 (-4t + 4t2) = 224 Solving -4t + 4t2 = 224 Solving for variable 't'. Reorder the terms: -224 + -4t + 4t2 = 224 + -224 Combine like terms: 224 + -224 = 0 -224 + -4t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + -1t + t2) = 0 Factor a trinomial. 4((-7 + -1t)(8 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve: Simplifying -7 + -1t = 0 Solving -7 + -1t = 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 + -1t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t = 0 + 7 -1t = 0 + 7 Combine like terms: 0 + 7 = 7 -1t = 7 Divide each side by '-1'. t = -7 Simplifying t = -7Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8Solution
t = {-7, 8}
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