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Simplifying 16t2 + 4t = 600 Reorder the terms: 4t + 16t2 = 600 Solving 4t + 16t2 = 600 Solving for variable 't'. Reorder the terms: -600 + 4t + 16t2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-150 + t + 4t2) = 0 Factor a trinomial. 4((-25 + -4t)(6 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -4t)' equal to zero and attempt to solve: Simplifying -25 + -4t = 0 Solving -25 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -4t = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4t = 0 + 25 -4t = 0 + 25 Combine like terms: 0 + 25 = 25 -4t = 25 Divide each side by '-4'. t = -6.25 Simplifying t = -6.25Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-6.25, 6}
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