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Simplifying 30 = 128t + -16t2 Solving 30 = 128t + -16t2 Solving for variable 't'. Reorder the terms: 30 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 30 + -128t + 16t2 = 0 + -16t2 + 16t2 30 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 30 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -64t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -64t + 8t2)' equal to zero and attempt to solve: Simplifying 15 + -64t + 8t2 = 0 Solving 15 + -64t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -8t + t2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -8t + -1.875 + t2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -8t + t2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -8t + t2 = 0 + -1.875 -8t + t2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -8t + t2 = -1.875 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -1.875 + 16 Reorder the terms: 16 + -8t + t2 = -1.875 + 16 Combine like terms: -1.875 + 16 = 14.125 16 + -8t + t2 = 14.125 Factor a perfect square on the left side: (t + -4)(t + -4) = 14.125 Calculate the square root of the right side: 3.758324095 Break this problem into two subproblems by setting (t + -4) equal to 3.758324095 and -3.758324095.Subproblem 1
t + -4 = 3.758324095 Simplifying t + -4 = 3.758324095 Reorder the terms: -4 + t = 3.758324095 Solving -4 + t = 3.758324095 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.758324095 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.758324095 + 4 t = 3.758324095 + 4 Combine like terms: 3.758324095 + 4 = 7.758324095 t = 7.758324095 Simplifying t = 7.758324095Subproblem 2
t + -4 = -3.758324095 Simplifying t + -4 = -3.758324095 Reorder the terms: -4 + t = -3.758324095 Solving -4 + t = -3.758324095 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.758324095 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.758324095 + 4 t = -3.758324095 + 4 Combine like terms: -3.758324095 + 4 = 0.241675905 t = 0.241675905 Simplifying t = 0.241675905Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.758324095, 0.241675905}Solution
t = {7.758324095, 0.241675905}
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