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Simplifying t2 + 16t + -48 = 0 Reorder the terms: -48 + 16t + t2 = 0 Solving -48 + 16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 16t + 48 + t2 = 0 + 48 Reorder the terms: -48 + 48 + 16t + t2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 16t + t2 = 0 + 48 16t + t2 = 0 + 48 Combine like terms: 0 + 48 = 48 16t + t2 = 48 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = 48 + 64 Reorder the terms: 64 + 16t + t2 = 48 + 64 Combine like terms: 48 + 64 = 112 64 + 16t + t2 = 112 Factor a perfect square on the left side: (t + 8)(t + 8) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (t + 8) equal to 10.583005244 and -10.583005244.Subproblem 1
t + 8 = 10.583005244 Simplifying t + 8 = 10.583005244 Reorder the terms: 8 + t = 10.583005244 Solving 8 + t = 10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 10.583005244 + -8 Combine like terms: 8 + -8 = 0 0 + t = 10.583005244 + -8 t = 10.583005244 + -8 Combine like terms: 10.583005244 + -8 = 2.583005244 t = 2.583005244 Simplifying t = 2.583005244Subproblem 2
t + 8 = -10.583005244 Simplifying t + 8 = -10.583005244 Reorder the terms: 8 + t = -10.583005244 Solving 8 + t = -10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -10.583005244 + -8 Combine like terms: 8 + -8 = 0 0 + t = -10.583005244 + -8 t = -10.583005244 + -8 Combine like terms: -10.583005244 + -8 = -18.583005244 t = -18.583005244 Simplifying t = -18.583005244Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.583005244, -18.583005244}
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