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Simplifying 3000 = -16t2 + 480t + 10 Reorder the terms: 3000 = 10 + 480t + -16t2 Solving 3000 = 10 + 480t + -16t2 Solving for variable 't'. Combine like terms: 3000 + -10 = 2990 2990 + -480t + 16t2 = 10 + 480t + -16t2 + -10 + -480t + 16t2 Reorder the terms: 2990 + -480t + 16t2 = 10 + -10 + 480t + -480t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 2990 + -480t + 16t2 = 0 + 480t + -480t + -16t2 + 16t2 2990 + -480t + 16t2 = 480t + -480t + -16t2 + 16t2 Combine like terms: 480t + -480t = 0 2990 + -480t + 16t2 = 0 + -16t2 + 16t2 2990 + -480t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2990 + -480t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1495 + -240t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1495 + -240t + 8t2)' equal to zero and attempt to solve: Simplifying 1495 + -240t + 8t2 = 0 Solving 1495 + -240t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 186.875 + -30t + t2 = 0 Move the constant term to the right: Add '-186.875' to each side of the equation. 186.875 + -30t + -186.875 + t2 = 0 + -186.875 Reorder the terms: 186.875 + -186.875 + -30t + t2 = 0 + -186.875 Combine like terms: 186.875 + -186.875 = 0.000 0.000 + -30t + t2 = 0 + -186.875 -30t + t2 = 0 + -186.875 Combine like terms: 0 + -186.875 = -186.875 -30t + t2 = -186.875 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = -186.875 + 225 Reorder the terms: 225 + -30t + t2 = -186.875 + 225 Combine like terms: -186.875 + 225 = 38.125 225 + -30t + t2 = 38.125 Factor a perfect square on the left side: (t + -15)(t + -15) = 38.125 Calculate the square root of the right side: 6.174544518 Break this problem into two subproblems by setting (t + -15) equal to 6.174544518 and -6.174544518.Subproblem 1
t + -15 = 6.174544518 Simplifying t + -15 = 6.174544518 Reorder the terms: -15 + t = 6.174544518 Solving -15 + t = 6.174544518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 6.174544518 + 15 Combine like terms: -15 + 15 = 0 0 + t = 6.174544518 + 15 t = 6.174544518 + 15 Combine like terms: 6.174544518 + 15 = 21.174544518 t = 21.174544518 Simplifying t = 21.174544518Subproblem 2
t + -15 = -6.174544518 Simplifying t + -15 = -6.174544518 Reorder the terms: -15 + t = -6.174544518 Solving -15 + t = -6.174544518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -6.174544518 + 15 Combine like terms: -15 + 15 = 0 0 + t = -6.174544518 + 15 t = -6.174544518 + 15 Combine like terms: -6.174544518 + 15 = 8.825455482 t = 8.825455482 Simplifying t = 8.825455482Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.174544518, 8.825455482}Solution
t = {21.174544518, 8.825455482}
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