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Simplifying 64 = -16t2 + 96t + 4 Reorder the terms: 64 = 4 + 96t + -16t2 Solving 64 = 4 + 96t + -16t2 Solving for variable 't'. Combine like terms: 64 + -4 = 60 60 + -96t + 16t2 = 4 + 96t + -16t2 + -4 + -96t + 16t2 Reorder the terms: 60 + -96t + 16t2 = 4 + -4 + 96t + -96t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 60 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 60 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 60 + -96t + 16t2 = 0 + -16t2 + 16t2 60 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 60 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + -24t + 4t2)' equal to zero and attempt to solve: Simplifying 15 + -24t + 4t2 = 0 Solving 15 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -6t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -6t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -6t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -6t + t2 = 0 + -3.75 -6t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -6t + t2 = -3.75 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 = -3.75 + 9 Reorder the terms: 9 + -6t + t2 = -3.75 + 9 Combine like terms: -3.75 + 9 = 5.25 9 + -6t + t2 = 5.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (t + -3) equal to 2.291287847 and -2.291287847.Subproblem 1
t + -3 = 2.291287847 Simplifying t + -3 = 2.291287847 Reorder the terms: -3 + t = 2.291287847 Solving -3 + t = 2.291287847 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 = 2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.291287847 + 3 t = 2.291287847 + 3 Combine like terms: 2.291287847 + 3 = 5.291287847 t = 5.291287847 Simplifying t = 5.291287847Subproblem 2
t + -3 = -2.291287847 Simplifying t + -3 = -2.291287847 Reorder the terms: -3 + t = -2.291287847 Solving -3 + t = -2.291287847 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 = -2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.291287847 + 3 t = -2.291287847 + 3 Combine like terms: -2.291287847 + 3 = 0.708712153 t = 0.708712153 Simplifying t = 0.708712153Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.291287847, 0.708712153}Solution
t = {5.291287847, 0.708712153}
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