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Simplifying 0 = -4.9t2 + 8t + 10 Reorder the terms: 0 = 10 + 8t + -4.9t2 Solving 0 = 10 + 8t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -8t + 4.9t2 = 10 + 8t + -4.9t2 + -10 + -8t + 4.9t2 Reorder the terms: -10 + -8t + 4.9t2 = 10 + -10 + 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -8t + 4.9t2 = 0 + 8t + -8t + -4.9t2 + 4.9t2 -10 + -8t + 4.9t2 = 8t + -8t + -4.9t2 + 4.9t2 Combine like terms: 8t + -8t = 0 -10 + -8t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -8t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -8t + 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'. -2.040816327 + -1.632653061t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1.632653061t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1.632653061t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1.632653061t + t2 = 0 + 2.040816327 -1.632653061t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1.632653061t + t2 = 2.040816327 The t term is -1.632653061t. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061t + 0.6663890044 + t2 = 2.040816327 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061t + t2 = 2.040816327 + 0.6663890044 Combine like terms: 2.040816327 + 0.6663890044 = 2.7072053314 0.6663890044 + -1.632653061t + t2 = 2.7072053314 Factor a perfect square on the left side: (t + -0.8163265305)(t + -0.8163265305) = 2.7072053314 Calculate the square root of the right side: 1.645358724 Break this problem into two subproblems by setting (t + -0.8163265305) equal to 1.645358724 and -1.645358724.Subproblem 1
t + -0.8163265305 = 1.645358724 Simplifying t + -0.8163265305 = 1.645358724 Reorder the terms: -0.8163265305 + t = 1.645358724 Solving -0.8163265305 + t = 1.645358724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = 1.645358724 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = 1.645358724 + 0.8163265305 t = 1.645358724 + 0.8163265305 Combine like terms: 1.645358724 + 0.8163265305 = 2.4616852545 t = 2.4616852545 Simplifying t = 2.4616852545Subproblem 2
t + -0.8163265305 = -1.645358724 Simplifying t + -0.8163265305 = -1.645358724 Reorder the terms: -0.8163265305 + t = -1.645358724 Solving -0.8163265305 + t = -1.645358724 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + t = -1.645358724 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + t = -1.645358724 + 0.8163265305 t = -1.645358724 + 0.8163265305 Combine like terms: -1.645358724 + 0.8163265305 = -0.8290321935 t = -0.8290321935 Simplifying t = -0.8290321935Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.4616852545, -0.8290321935}
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