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Simplifying 60 = -16t2 + 96t + 12 Reorder the terms: 60 = 12 + 96t + -16t2 Solving 60 = 12 + 96t + -16t2 Solving for variable 't'. Combine like terms: 60 + -12 = 48 48 + -96t + 16t2 = 12 + 96t + -16t2 + -12 + -96t + 16t2 Reorder the terms: 48 + -96t + 16t2 = 12 + -12 + 96t + -96t + -16t2 + 16t2 Combine like terms: 12 + -12 = 0 48 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 48 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 48 + -96t + 16t2 = 0 + -16t2 + 16t2 48 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 48 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(3 + -6t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -6t + t2)' equal to zero and attempt to solve: Simplifying 3 + -6t + t2 = 0 Solving 3 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -6t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6t + t2 = 0 + -3 -6t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6t + t2 = -3 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 = -3 + 9 Reorder the terms: 9 + -6t + t2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6t + t2 = 6 Factor a perfect square on the left side: (t + -3)(t + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
t + -3 = 2.449489743 Simplifying t + -3 = 2.449489743 Reorder the terms: -3 + t = 2.449489743 Solving -3 + t = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.449489743 + 3 t = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 t = 5.449489743 Simplifying t = 5.449489743Subproblem 2
t + -3 = -2.449489743 Simplifying t + -3 = -2.449489743 Reorder the terms: -3 + t = -2.449489743 Solving -3 + t = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.449489743 + 3 t = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 t = 0.550510257 Simplifying t = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.449489743, 0.550510257}Solution
t = {5.449489743, 0.550510257}
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