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Simplifying -4.9t2 + 34.3t + 1.5 = 50.5 Reorder the terms: 1.5 + 34.3t + -4.9t2 = 50.5 Solving 1.5 + 34.3t + -4.9t2 = 50.5 Solving for variable 't'. Reorder the terms: 1.5 + -50.5 + 34.3t + -4.9t2 = 50.5 + -50.5 Combine like terms: 1.5 + -50.5 = -49 -49 + 34.3t + -4.9t2 = 50.5 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 -49 + 34.3t + -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'. 10 + -7t + t2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + -7t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7t + t2 = 0 + -10 -7t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7t + t2 = -10 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -10 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -10 + 12.25 Combine like terms: -10 + 12.25 = 2.25 12.25 + -7t + t2 = 2.25 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (t + -3.5) equal to 1.5 and -1.5.Subproblem 1
t + -3.5 = 1.5 Simplifying t + -3.5 = 1.5 Reorder the terms: -3.5 + t = 1.5 Solving -3.5 + t = 1.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 1.5 + 3.5 t = 1.5 + 3.5 Combine like terms: 1.5 + 3.5 = 5 t = 5 Simplifying t = 5Subproblem 2
t + -3.5 = -1.5 Simplifying t + -3.5 = -1.5 Reorder the terms: -3.5 + t = -1.5 Solving -3.5 + t = -1.5 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -1.5 + 3.5 t = -1.5 + 3.5 Combine like terms: -1.5 + 3.5 = 2 t = 2 Simplifying t = 2Solution
The solution to the problem is based on the solutions from the subproblems. t = {5, 2}
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