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Simplifying 48 = -16t2 + -32t + 320 Reorder the terms: 48 = 320 + -32t + -16t2 Solving 48 = 320 + -32t + -16t2 Solving for variable 't'. Combine like terms: 48 + -320 = -272 -272 + 32t + 16t2 = 320 + -32t + -16t2 + -320 + 32t + 16t2 Reorder the terms: -272 + 32t + 16t2 = 320 + -320 + -32t + 32t + -16t2 + 16t2 Combine like terms: 320 + -320 = 0 -272 + 32t + 16t2 = 0 + -32t + 32t + -16t2 + 16t2 -272 + 32t + 16t2 = -32t + 32t + -16t2 + 16t2 Combine like terms: -32t + 32t = 0 -272 + 32t + 16t2 = 0 + -16t2 + 16t2 -272 + 32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -272 + 32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-17 + 2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-17 + 2t + t2)' equal to zero and attempt to solve: Simplifying -17 + 2t + t2 = 0 Solving -17 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 2t + 17 + t2 = 0 + 17 Reorder the terms: -17 + 17 + 2t + t2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2t + t2 = 0 + 17 2t + t2 = 0 + 17 Combine like terms: 0 + 17 = 17 2t + t2 = 17 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 17 + 1 Reorder the terms: 1 + 2t + t2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2t + t2 = 18 Factor a perfect square on the left side: (t + 1)(t + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
t + 1 = 4.242640687 Simplifying t + 1 = 4.242640687 Reorder the terms: 1 + t = 4.242640687 Solving 1 + t = 4.242640687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + t = 4.242640687 + -1 t = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 t = 3.242640687 Simplifying t = 3.242640687Subproblem 2
t + 1 = -4.242640687 Simplifying t + 1 = -4.242640687 Reorder the terms: 1 + t = -4.242640687 Solving 1 + t = -4.242640687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + t = -4.242640687 + -1 t = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 t = -5.242640687 Simplifying t = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.242640687, -5.242640687}Solution
t = {3.242640687, -5.242640687}
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