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Simplifying 16t2 + -128t + 208 = 0 Reorder the terms: 208 + -128t + 16t2 = 0 Solving 208 + -128t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(13 + -8t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(13 + -8t + t2)' equal to zero and attempt to solve: Simplifying 13 + -8t + t2 = 0 Solving 13 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8t + -13 + t2 = 0 + -13 Reorder the terms: 13 + -13 + -8t + t2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8t + t2 = 0 + -13 -8t + t2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8t + t2 = -13 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 = -13 + 16 Reorder the terms: 16 + -8t + t2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8t + t2 = 3 Factor a perfect square on the left side: (t + -4)(t + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
t + -4 = 1.732050808 Simplifying t + -4 = 1.732050808 Reorder the terms: -4 + t = 1.732050808 Solving -4 + t = 1.732050808 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 = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.732050808 + 4 t = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 t = 5.732050808 Simplifying t = 5.732050808Subproblem 2
t + -4 = -1.732050808 Simplifying t + -4 = -1.732050808 Reorder the terms: -4 + t = -1.732050808 Solving -4 + t = -1.732050808 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 = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.732050808 + 4 t = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 t = 2.267949192 Simplifying t = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.732050808, 2.267949192}Solution
t = {5.732050808, 2.267949192}
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