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Simplifying 6 = -4.9t2 + 3t + 10 Reorder the terms: 6 = 10 + 3t + -4.9t2 Solving 6 = 10 + 3t + -4.9t2 Solving for variable 't'. Combine like terms: 6 + -10 = -4 -4 + -3t + 4.9t2 = 10 + 3t + -4.9t2 + -10 + -3t + 4.9t2 Reorder the terms: -4 + -3t + 4.9t2 = 10 + -10 + 3t + -3t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -4 + -3t + 4.9t2 = 0 + 3t + -3t + -4.9t2 + 4.9t2 -4 + -3t + 4.9t2 = 3t + -3t + -4.9t2 + 4.9t2 Combine like terms: 3t + -3t = 0 -4 + -3t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -4 + -3t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -4 + -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'. -0.8163265306 + -0.612244898t + t2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -0.612244898t + 0.8163265306 + t2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -0.612244898t + t2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -0.612244898t + t2 = 0 + 0.8163265306 -0.612244898t + t2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -0.612244898t + t2 = 0.8163265306 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 = 0.8163265306 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898t + t2 = 0.8163265306 + 0.09371095378 Combine like terms: 0.8163265306 + 0.09371095378 = 0.91003748438 0.09371095378 + -0.612244898t + t2 = 0.91003748438 Factor a perfect square on the left side: (t + -0.306122449)(t + -0.306122449) = 0.91003748438 Calculate the square root of the right side: 0.953958848 Break this problem into two subproblems by setting (t + -0.306122449) equal to 0.953958848 and -0.953958848.Subproblem 1
t + -0.306122449 = 0.953958848 Simplifying t + -0.306122449 = 0.953958848 Reorder the terms: -0.306122449 + t = 0.953958848 Solving -0.306122449 + t = 0.953958848 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 = 0.953958848 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = 0.953958848 + 0.306122449 t = 0.953958848 + 0.306122449 Combine like terms: 0.953958848 + 0.306122449 = 1.260081297 t = 1.260081297 Simplifying t = 1.260081297Subproblem 2
t + -0.306122449 = -0.953958848 Simplifying t + -0.306122449 = -0.953958848 Reorder the terms: -0.306122449 + t = -0.953958848 Solving -0.306122449 + t = -0.953958848 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 = -0.953958848 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = -0.953958848 + 0.306122449 t = -0.953958848 + 0.306122449 Combine like terms: -0.953958848 + 0.306122449 = -0.647836399 t = -0.647836399 Simplifying t = -0.647836399Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.260081297, -0.647836399}
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