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Simplifying 0 = -4.9t2 + 19.6t + 58.8 Reorder the terms: 0 = 58.8 + 19.6t + -4.9t2 Solving 0 = 58.8 + 19.6t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -58.8 = -58.8 -58.8 + -19.6t + 4.9t2 = 58.8 + 19.6t + -4.9t2 + -58.8 + -19.6t + 4.9t2 Reorder the terms: -58.8 + -19.6t + 4.9t2 = 58.8 + -58.8 + 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 58.8 + -58.8 = 0.0 -58.8 + -19.6t + 4.9t2 = 0.0 + 19.6t + -19.6t + -4.9t2 + 4.9t2 -58.8 + -19.6t + 4.9t2 = 19.6t + -19.6t + -4.9t2 + 4.9t2 Combine like terms: 19.6t + -19.6t = 0.0 -58.8 + -19.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -58.8 + -19.6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -58.8 + -19.6t + 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'. -12 + -4t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -4t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -4t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4t + t2 = 0 + 12 -4t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -4t + t2 = 12 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 12 + 4 Reorder the terms: 4 + -4t + t2 = 12 + 4 Combine like terms: 12 + 4 = 16 4 + -4t + t2 = 16 Factor a perfect square on the left side: (t + -2)(t + -2) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (t + -2) equal to 4 and -4.Subproblem 1
t + -2 = 4 Simplifying t + -2 = 4 Reorder the terms: -2 + t = 4 Solving -2 + t = 4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4 + 2 t = 4 + 2 Combine like terms: 4 + 2 = 6 t = 6 Simplifying t = 6Subproblem 2
t + -2 = -4 Simplifying t + -2 = -4 Reorder the terms: -2 + t = -4 Solving -2 + t = -4 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4 + 2 t = -4 + 2 Combine like terms: -4 + 2 = -2 t = -2 Simplifying t = -2Solution
The solution to the problem is based on the solutions from the subproblems. t = {6, -2}
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