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Simplifying 600t2 + 60t + -3 = 0 Reorder the terms: -3 + 60t + 600t2 = 0 Solving -3 + 60t + 600t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 20t + 200t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 20t + 200t2)' equal to zero and attempt to solve: Simplifying -1 + 20t + 200t2 = 0 Solving -1 + 20t + 200t2 = 0 Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. -0.005 + 0.1t + t2 = 0.00 Move the constant term to the right: Add '0.005' to each side of the equation. -0.005 + 0.1t + 0.005 + t2 = 0.00 + 0.005 Reorder the terms: -0.005 + 0.005 + 0.1t + t2 = 0.00 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + 0.1t + t2 = 0.00 + 0.005 0.1t + t2 = 0.00 + 0.005 Combine like terms: 0.00 + 0.005 = 0.005 0.1t + t2 = 0.005 The t term is 0.1t. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1t + 0.0025 + t2 = 0.005 + 0.0025 Reorder the terms: 0.0025 + 0.1t + t2 = 0.005 + 0.0025 Combine like terms: 0.005 + 0.0025 = 0.0075 0.0025 + 0.1t + t2 = 0.0075 Factor a perfect square on the left side: (t + 0.05)(t + 0.05) = 0.0075 Calculate the square root of the right side: 0.08660254 Break this problem into two subproblems by setting (t + 0.05) equal to 0.08660254 and -0.08660254.Subproblem 1
t + 0.05 = 0.08660254 Simplifying t + 0.05 = 0.08660254 Reorder the terms: 0.05 + t = 0.08660254 Solving 0.05 + t = 0.08660254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + t = 0.08660254 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + t = 0.08660254 + -0.05 t = 0.08660254 + -0.05 Combine like terms: 0.08660254 + -0.05 = 0.03660254 t = 0.03660254 Simplifying t = 0.03660254Subproblem 2
t + 0.05 = -0.08660254 Simplifying t + 0.05 = -0.08660254 Reorder the terms: 0.05 + t = -0.08660254 Solving 0.05 + t = -0.08660254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + t = -0.08660254 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + t = -0.08660254 + -0.05 t = -0.08660254 + -0.05 Combine like terms: -0.08660254 + -0.05 = -0.13660254 t = -0.13660254 Simplifying t = -0.13660254Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.03660254, -0.13660254}Solution
t = {0.03660254, -0.13660254}
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