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Simplifying 7 + 16t + -4.9t2 = 0 Solving 7 + 16t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.428571429 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -3.265306122t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -3.265306122t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -3.265306122t + t2 = 0 + 1.428571429 -3.265306122t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -3.265306122t + t2 = 1.428571429 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 = 1.428571429 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 1.428571429 + 2.665556018 Combine like terms: 1.428571429 + 2.665556018 = 4.094127447 2.665556018 + -3.265306122t + t2 = 4.094127447 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 4.094127447 Calculate the square root of the right side: 2.02339503 Break this problem into two subproblems by setting (t + -1.632653061) equal to 2.02339503 and -2.02339503.Subproblem 1
t + -1.632653061 = 2.02339503 Simplifying t + -1.632653061 = 2.02339503 Reorder the terms: -1.632653061 + t = 2.02339503 Solving -1.632653061 + t = 2.02339503 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 = 2.02339503 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 2.02339503 + 1.632653061 t = 2.02339503 + 1.632653061 Combine like terms: 2.02339503 + 1.632653061 = 3.656048091 t = 3.656048091 Simplifying t = 3.656048091Subproblem 2
t + -1.632653061 = -2.02339503 Simplifying t + -1.632653061 = -2.02339503 Reorder the terms: -1.632653061 + t = -2.02339503 Solving -1.632653061 + t = -2.02339503 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 = -2.02339503 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -2.02339503 + 1.632653061 t = -2.02339503 + 1.632653061 Combine like terms: -2.02339503 + 1.632653061 = -0.390741969 t = -0.390741969 Simplifying t = -0.390741969Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.656048091, -0.390741969}
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