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Simplifying 0 = 4.9t2 + -16t + -3 Reorder the terms: 0 = -3 + -16t + 4.9t2 Solving 0 = -3 + -16t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 3 = 3 3 + 16t + -4.9t2 = -3 + -16t + 4.9t2 + 3 + 16t + -4.9t2 Reorder the terms: 3 + 16t + -4.9t2 = -3 + 3 + -16t + 16t + 4.9t2 + -4.9t2 Combine like terms: -3 + 3 = 0 3 + 16t + -4.9t2 = 0 + -16t + 16t + 4.9t2 + -4.9t2 3 + 16t + -4.9t2 = -16t + 16t + 4.9t2 + -4.9t2 Combine like terms: -16t + 16t = 0 3 + 16t + -4.9t2 = 0 + 4.9t2 + -4.9t2 3 + 16t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 3 + 16t + -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'. -0.612244898 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -3.265306122t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -3.265306122t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -3.265306122t + t2 = 0 + 0.612244898 -3.265306122t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -3.265306122t + t2 = 0.612244898 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = 0.612244898 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 0.612244898 + 2.665556018 Combine like terms: 0.612244898 + 2.665556018 = 3.277800916 2.665556018 + -3.265306122t + t2 = 3.277800916 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 3.277800916 Calculate the square root of the right side: 1.810469805 Break this problem into two subproblems by setting (t + -1.632653061) equal to 1.810469805 and -1.810469805.Subproblem 1
t + -1.632653061 = 1.810469805 Simplifying t + -1.632653061 = 1.810469805 Reorder the terms: -1.632653061 + t = 1.810469805 Solving -1.632653061 + t = 1.810469805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.810469805 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.810469805 + 1.632653061 t = 1.810469805 + 1.632653061 Combine like terms: 1.810469805 + 1.632653061 = 3.443122866 t = 3.443122866 Simplifying t = 3.443122866Subproblem 2
t + -1.632653061 = -1.810469805 Simplifying t + -1.632653061 = -1.810469805 Reorder the terms: -1.632653061 + t = -1.810469805 Solving -1.632653061 + t = -1.810469805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.810469805 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.810469805 + 1.632653061 t = -1.810469805 + 1.632653061 Combine like terms: -1.810469805 + 1.632653061 = -0.177816744 t = -0.177816744 Simplifying t = -0.177816744Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.443122866, -0.177816744}
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