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Simplifying -5t2 + 55t + 50 = 100 Reorder the terms: 50 + 55t + -5t2 = 100 Solving 50 + 55t + -5t2 = 100 Solving for variable 't'. Reorder the terms: 50 + -100 + 55t + -5t2 = 100 + -100 Combine like terms: 50 + -100 = -50 -50 + 55t + -5t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -50 + 55t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + 11t + -1t2) = 0 Factor a trinomial. 5((-10 + t)(1 + -1t)) = 0 Ignore the factor 5.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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {10, 1}
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