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Simplifying 0 = -16t2 + 96t + 2500 Reorder the terms: 0 = 2500 + 96t + -16t2 Solving 0 = 2500 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2500 = -2500 -2500 + -96t + 16t2 = 2500 + 96t + -16t2 + -2500 + -96t + 16t2 Reorder the terms: -2500 + -96t + 16t2 = 2500 + -2500 + 96t + -96t + -16t2 + 16t2 Combine like terms: 2500 + -2500 = 0 -2500 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -2500 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -2500 + -96t + 16t2 = 0 + -16t2 + 16t2 -2500 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2500 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-625 + -24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-625 + -24t + 4t2)' equal to zero and attempt to solve: Simplifying -625 + -24t + 4t2 = 0 Solving -625 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -156.25 + -6t + t2 = 0 Move the constant term to the right: Add '156.25' to each side of the equation. -156.25 + -6t + 156.25 + t2 = 0 + 156.25 Reorder the terms: -156.25 + 156.25 + -6t + t2 = 0 + 156.25 Combine like terms: -156.25 + 156.25 = 0.00 0.00 + -6t + t2 = 0 + 156.25 -6t + t2 = 0 + 156.25 Combine like terms: 0 + 156.25 = 156.25 -6t + t2 = 156.25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 156.25 + 9 Reorder the terms: 9 + -6t + t2 = 156.25 + 9 Combine like terms: 156.25 + 9 = 165.25 9 + -6t + t2 = 165.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 165.25 Calculate the square root of the right side: 12.854960132 Break this problem into two subproblems by setting (t + -3) equal to 12.854960132 and -12.854960132.Subproblem 1
t + -3 = 12.854960132 Simplifying t + -3 = 12.854960132 Reorder the terms: -3 + t = 12.854960132 Solving -3 + t = 12.854960132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 12.854960132 + 3 Combine like terms: -3 + 3 = 0 0 + t = 12.854960132 + 3 t = 12.854960132 + 3 Combine like terms: 12.854960132 + 3 = 15.854960132 t = 15.854960132 Simplifying t = 15.854960132Subproblem 2
t + -3 = -12.854960132 Simplifying t + -3 = -12.854960132 Reorder the terms: -3 + t = -12.854960132 Solving -3 + t = -12.854960132 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -12.854960132 + 3 Combine like terms: -3 + 3 = 0 0 + t = -12.854960132 + 3 t = -12.854960132 + 3 Combine like terms: -12.854960132 + 3 = -9.854960132 t = -9.854960132 Simplifying t = -9.854960132Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.854960132, -9.854960132}Solution
t = {15.854960132, -9.854960132}
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