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Simplifying 100 = -16t2 + 96t + 2 Reorder the terms: 100 = 2 + 96t + -16t2 Solving 100 = 2 + 96t + -16t2 Solving for variable 't'. Combine like terms: 100 + -2 = 98 98 + -96t + 16t2 = 2 + 96t + -16t2 + -2 + -96t + 16t2 Reorder the terms: 98 + -96t + 16t2 = 2 + -2 + 96t + -96t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 98 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 98 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 98 + -96t + 16t2 = 0 + -16t2 + 16t2 98 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 98 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -48t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + -48t + 8t2)' equal to zero and attempt to solve: Simplifying 49 + -48t + 8t2 = 0 Solving 49 + -48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.125 + -6t + t2 = 0 Move the constant term to the right: Add '-6.125' to each side of the equation. 6.125 + -6t + -6.125 + t2 = 0 + -6.125 Reorder the terms: 6.125 + -6.125 + -6t + t2 = 0 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + -6t + t2 = 0 + -6.125 -6t + t2 = 0 + -6.125 Combine like terms: 0 + -6.125 = -6.125 -6t + t2 = -6.125 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 = -6.125 + 9 Reorder the terms: 9 + -6t + t2 = -6.125 + 9 Combine like terms: -6.125 + 9 = 2.875 9 + -6t + t2 = 2.875 Factor a perfect square on the left side: (t + -3)(t + -3) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (t + -3) equal to 1.695582496 and -1.695582496.Subproblem 1
t + -3 = 1.695582496 Simplifying t + -3 = 1.695582496 Reorder the terms: -3 + t = 1.695582496 Solving -3 + t = 1.695582496 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 = 1.695582496 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.695582496 + 3 t = 1.695582496 + 3 Combine like terms: 1.695582496 + 3 = 4.695582496 t = 4.695582496 Simplifying t = 4.695582496Subproblem 2
t + -3 = -1.695582496 Simplifying t + -3 = -1.695582496 Reorder the terms: -3 + t = -1.695582496 Solving -3 + t = -1.695582496 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 = -1.695582496 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.695582496 + 3 t = -1.695582496 + 3 Combine like terms: -1.695582496 + 3 = 1.304417504 t = 1.304417504 Simplifying t = 1.304417504Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.695582496, 1.304417504}Solution
t = {4.695582496, 1.304417504}
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