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Simplifying -4.9t2 + 34.3t + -58.8 = 0 Reorder the terms: -58.8 + 34.3t + -4.9t2 = 0 Solving -58.8 + 34.3t + -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'. 12 + -7t + t2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + -7t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7t + t2 = 0 + -12 -7t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7t + t2 = -12 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 = -12 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -12 + 12.25 Combine like terms: -12 + 12.25 = 0.25 12.25 + -7t + t2 = 0.25 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (t + -3.5) equal to 0.5 and -0.5.Subproblem 1
t + -3.5 = 0.5 Simplifying t + -3.5 = 0.5 Reorder the terms: -3.5 + t = 0.5 Solving -3.5 + t = 0.5 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 = 0.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 0.5 + 3.5 t = 0.5 + 3.5 Combine like terms: 0.5 + 3.5 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -3.5 = -0.5 Simplifying t + -3.5 = -0.5 Reorder the terms: -3.5 + t = -0.5 Solving -3.5 + t = -0.5 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 = -0.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -0.5 + 3.5 t = -0.5 + 3.5 Combine like terms: -0.5 + 3.5 = 3 t = 3 Simplifying t = 3Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, 3}
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