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Simplifying 0 = -16t2 + 96t + 116 Reorder the terms: 0 = 116 + 96t + -16t2 Solving 0 = 116 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -116 = -116 -116 + -96t + 16t2 = 116 + 96t + -16t2 + -116 + -96t + 16t2 Reorder the terms: -116 + -96t + 16t2 = 116 + -116 + 96t + -96t + -16t2 + 16t2 Combine like terms: 116 + -116 = 0 -116 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -116 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -116 + -96t + 16t2 = 0 + -16t2 + 16t2 -116 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -116 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-29 + -24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-29 + -24t + 4t2)' equal to zero and attempt to solve: Simplifying -29 + -24t + 4t2 = 0 Solving -29 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -6t + t2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -6t + 7.25 + t2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -6t + t2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -6t + t2 = 0 + 7.25 -6t + t2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -6t + t2 = 7.25 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 = 7.25 + 9 Reorder the terms: 9 + -6t + t2 = 7.25 + 9 Combine like terms: 7.25 + 9 = 16.25 9 + -6t + t2 = 16.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (t + -3) equal to 4.031128874 and -4.031128874.Subproblem 1
t + -3 = 4.031128874 Simplifying t + -3 = 4.031128874 Reorder the terms: -3 + t = 4.031128874 Solving -3 + t = 4.031128874 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 = 4.031128874 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.031128874 + 3 t = 4.031128874 + 3 Combine like terms: 4.031128874 + 3 = 7.031128874 t = 7.031128874 Simplifying t = 7.031128874Subproblem 2
t + -3 = -4.031128874 Simplifying t + -3 = -4.031128874 Reorder the terms: -3 + t = -4.031128874 Solving -3 + t = -4.031128874 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 = -4.031128874 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.031128874 + 3 t = -4.031128874 + 3 Combine like terms: -4.031128874 + 3 = -1.031128874 t = -1.031128874 Simplifying t = -1.031128874Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.031128874, -1.031128874}Solution
t = {7.031128874, -1.031128874}
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