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Simplifying 10 = (-16) * t + 4.9t2 Solving 10 = -16t + 4.9t2 Solving for variable 't'. Reorder the terms: 10 + 16t + -4.9t2 = -16t + 16t + 4.9t2 + -4.9t2 Combine like terms: -16t + 16t = 0 10 + 16t + -4.9t2 = 0 + 4.9t2 + -4.9t2 10 + 16t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 10 + 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'. -2.040816327 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -3.265306122t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -3.265306122t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -3.265306122t + t2 = 0 + 2.040816327 -3.265306122t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -3.265306122t + t2 = 2.040816327 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 = 2.040816327 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 2.040816327 + 2.665556018 Combine like terms: 2.040816327 + 2.665556018 = 4.706372345 2.665556018 + -3.265306122t + t2 = 4.706372345 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 4.706372345 Calculate the square root of the right side: 2.169417513 Break this problem into two subproblems by setting (t + -1.632653061) equal to 2.169417513 and -2.169417513.Subproblem 1
t + -1.632653061 = 2.169417513 Simplifying t + -1.632653061 = 2.169417513 Reorder the terms: -1.632653061 + t = 2.169417513 Solving -1.632653061 + t = 2.169417513 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 = 2.169417513 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 2.169417513 + 1.632653061 t = 2.169417513 + 1.632653061 Combine like terms: 2.169417513 + 1.632653061 = 3.802070574 t = 3.802070574 Simplifying t = 3.802070574Subproblem 2
t + -1.632653061 = -2.169417513 Simplifying t + -1.632653061 = -2.169417513 Reorder the terms: -1.632653061 + t = -2.169417513 Solving -1.632653061 + t = -2.169417513 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 = -2.169417513 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -2.169417513 + 1.632653061 t = -2.169417513 + 1.632653061 Combine like terms: -2.169417513 + 1.632653061 = -0.536764452 t = -0.536764452 Simplifying t = -0.536764452Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.802070574, -0.536764452}
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