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Simplifying 6t + 4.9t2 = 40 Solving 6t + 4.9t2 = 40 Solving for variable 't'. Reorder the terms: -40 + 6t + 4.9t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 6t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -8.163265306 + 1.224489796t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + 1.224489796t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + 1.224489796t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + 1.224489796t + t2 = 0 + 8.163265306 1.224489796t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 1.224489796t + t2 = 8.163265306 The t term is 1.224489796t. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796t + 0.3748438151 + t2 = 8.163265306 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796t + t2 = 8.163265306 + 0.3748438151 Combine like terms: 8.163265306 + 0.3748438151 = 8.5381091211 0.3748438151 + 1.224489796t + t2 = 8.5381091211 Factor a perfect square on the left side: (t + 0.612244898)(t + 0.612244898) = 8.5381091211 Calculate the square root of the right side: 2.922004299 Break this problem into two subproblems by setting (t + 0.612244898) equal to 2.922004299 and -2.922004299.Subproblem 1
t + 0.612244898 = 2.922004299 Simplifying t + 0.612244898 = 2.922004299 Reorder the terms: 0.612244898 + t = 2.922004299 Solving 0.612244898 + t = 2.922004299 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + t = 2.922004299 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + t = 2.922004299 + -0.612244898 t = 2.922004299 + -0.612244898 Combine like terms: 2.922004299 + -0.612244898 = 2.309759401 t = 2.309759401 Simplifying t = 2.309759401Subproblem 2
t + 0.612244898 = -2.922004299 Simplifying t + 0.612244898 = -2.922004299 Reorder the terms: 0.612244898 + t = -2.922004299 Solving 0.612244898 + t = -2.922004299 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + t = -2.922004299 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + t = -2.922004299 + -0.612244898 t = -2.922004299 + -0.612244898 Combine like terms: -2.922004299 + -0.612244898 = -3.534249197 t = -3.534249197 Simplifying t = -3.534249197Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.309759401, -3.534249197}
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