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Simplifying 294 = 4.9t2 + 34.3t Reorder the terms: 294 = 34.3t + 4.9t2 Solving 294 = 34.3t + 4.9t2 Solving for variable 't'. Reorder the terms: 294 + -34.3t + -4.9t2 = 34.3t + -34.3t + 4.9t2 + -4.9t2 Combine like terms: 34.3t + -34.3t = 0.0 294 + -34.3t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 294 + -34.3t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 294 + -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'. -60 + 7t + t2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 7t + 60 + t2 = 0 + 60 Reorder the terms: -60 + 60 + 7t + t2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 7t + t2 = 0 + 60 7t + t2 = 0 + 60 Combine like terms: 0 + 60 = 60 7t + t2 = 60 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 = 60 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 60 + 12.25 Combine like terms: 60 + 12.25 = 72.25 12.25 + 7t + t2 = 72.25 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 72.25 Calculate the square root of the right side: 8.5 Break this problem into two subproblems by setting (t + 3.5) equal to 8.5 and -8.5.Subproblem 1
t + 3.5 = 8.5 Simplifying t + 3.5 = 8.5 Reorder the terms: 3.5 + t = 8.5 Solving 3.5 + t = 8.5 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 = 8.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 8.5 + -3.5 t = 8.5 + -3.5 Combine like terms: 8.5 + -3.5 = 5 t = 5 Simplifying t = 5Subproblem 2
t + 3.5 = -8.5 Simplifying t + 3.5 = -8.5 Reorder the terms: 3.5 + t = -8.5 Solving 3.5 + t = -8.5 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 = -8.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -8.5 + -3.5 t = -8.5 + -3.5 Combine like terms: -8.5 + -3.5 = -12 t = -12 Simplifying t = -12Solution
The solution to the problem is based on the solutions from the subproblems. t = {5, -12}
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