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Simplifying 3t2 + -96t + 3 = 0 Reorder the terms: 3 + -96t + 3t2 = 0 Solving 3 + -96t + 3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -32t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -32t + t2)' equal to zero and attempt to solve: Simplifying 1 + -32t + t2 = 0 Solving 1 + -32t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -32t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -32t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -32t + t2 = 0 + -1 -32t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -32t + t2 = -1 The t term is -32t. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32t + 256 + t2 = -1 + 256 Reorder the terms: 256 + -32t + t2 = -1 + 256 Combine like terms: -1 + 256 = 255 256 + -32t + t2 = 255 Factor a perfect square on the left side: (t + -16)(t + -16) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (t + -16) equal to 15.968719423 and -15.968719423.Subproblem 1
t + -16 = 15.968719423 Simplifying t + -16 = 15.968719423 Reorder the terms: -16 + t = 15.968719423 Solving -16 + t = 15.968719423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = 15.968719423 + 16 Combine like terms: -16 + 16 = 0 0 + t = 15.968719423 + 16 t = 15.968719423 + 16 Combine like terms: 15.968719423 + 16 = 31.968719423 t = 31.968719423 Simplifying t = 31.968719423Subproblem 2
t + -16 = -15.968719423 Simplifying t + -16 = -15.968719423 Reorder the terms: -16 + t = -15.968719423 Solving -16 + t = -15.968719423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + t = -15.968719423 + 16 Combine like terms: -16 + 16 = 0 0 + t = -15.968719423 + 16 t = -15.968719423 + 16 Combine like terms: -15.968719423 + 16 = 0.031280577 t = 0.031280577 Simplifying t = 0.031280577Solution
The solution to the problem is based on the solutions from the subproblems. t = {31.968719423, 0.031280577}Solution
t = {31.968719423, 0.031280577}
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