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Simplifying 80 = 128t + -16t2 Solving 80 = 128t + -16t2 Solving for variable 't'. Reorder the terms: 80 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 80 + -128t + 16t2 = 0 + -16t2 + 16t2 80 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 80 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(5 + -8t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + -8t + t2)' equal to zero and attempt to solve: Simplifying 5 + -8t + t2 = 0 Solving 5 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -8t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8t + t2 = 0 + -5 -8t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8t + t2 = -5 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 = -5 + 16 Reorder the terms: 16 + -8t + t2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8t + t2 = 11 Factor a perfect square on the left side: (t + -4)(t + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (t + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
t + -4 = 3.31662479 Simplifying t + -4 = 3.31662479 Reorder the terms: -4 + t = 3.31662479 Solving -4 + t = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.31662479 + 4 t = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 t = 7.31662479 Simplifying t = 7.31662479Subproblem 2
t + -4 = -3.31662479 Simplifying t + -4 = -3.31662479 Reorder the terms: -4 + t = -3.31662479 Solving -4 + t = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.31662479 + 4 t = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 t = 0.68337521 Simplifying t = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.31662479, 0.68337521}Solution
t = {7.31662479, 0.68337521}
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