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Simplifying 50 = 3t + 4.9t2 Solving 50 = 3t + 4.9t2 Solving for variable 't'. Reorder the terms: 50 + -3t + -4.9t2 = 3t + -3t + 4.9t2 + -4.9t2 Combine like terms: 3t + -3t = 0 50 + -3t + -4.9t2 = 0 + 4.9t2 + -4.9t2 50 + -3t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 50 + -3t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -10.20408163 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.612244898t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.612244898t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.612244898t + t2 = 0 + 10.20408163 0.612244898t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.612244898t + t2 = 10.20408163 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 10.20408163 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 10.20408163 + 0.09371095378 Combine like terms: 10.20408163 + 0.09371095378 = 10.29779258378 0.09371095378 + 0.612244898t + t2 = 10.29779258378 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 10.29779258378 Calculate the square root of the right side: 3.209017386 Break this problem into two subproblems by setting (t + 0.306122449) equal to 3.209017386 and -3.209017386.Subproblem 1
t + 0.306122449 = 3.209017386 Simplifying t + 0.306122449 = 3.209017386 Reorder the terms: 0.306122449 + t = 3.209017386 Solving 0.306122449 + t = 3.209017386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 3.209017386 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 3.209017386 + -0.306122449 t = 3.209017386 + -0.306122449 Combine like terms: 3.209017386 + -0.306122449 = 2.902894937 t = 2.902894937 Simplifying t = 2.902894937Subproblem 2
t + 0.306122449 = -3.209017386 Simplifying t + 0.306122449 = -3.209017386 Reorder the terms: 0.306122449 + t = -3.209017386 Solving 0.306122449 + t = -3.209017386 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -3.209017386 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -3.209017386 + -0.306122449 t = -3.209017386 + -0.306122449 Combine like terms: -3.209017386 + -0.306122449 = -3.515139835 t = -3.515139835 Simplifying t = -3.515139835Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.902894937, -3.515139835}
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