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Simplifying 6462 = 30t + 19t2 Solving 6462 = 30t + 19t2 Solving for variable 't'. Reorder the terms: 6462 + -30t + -19t2 = 30t + -30t + 19t2 + -19t2 Combine like terms: 30t + -30t = 0 6462 + -30t + -19t2 = 0 + 19t2 + -19t2 6462 + -30t + -19t2 = 19t2 + -19t2 Combine like terms: 19t2 + -19t2 = 0 6462 + -30t + -19t2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -340.1052632 + 1.578947368t + t2 = 0 Move the constant term to the right: Add '340.1052632' to each side of the equation. -340.1052632 + 1.578947368t + 340.1052632 + t2 = 0 + 340.1052632 Reorder the terms: -340.1052632 + 340.1052632 + 1.578947368t + t2 = 0 + 340.1052632 Combine like terms: -340.1052632 + 340.1052632 = 0.0000000 0.0000000 + 1.578947368t + t2 = 0 + 340.1052632 1.578947368t + t2 = 0 + 340.1052632 Combine like terms: 0 + 340.1052632 = 340.1052632 1.578947368t + t2 = 340.1052632 The t term is 1.578947368t. Take half its coefficient (0.789473684). Square it (0.6232686977) and add it to both sides. Add '0.6232686977' to each side of the equation. 1.578947368t + 0.6232686977 + t2 = 340.1052632 + 0.6232686977 Reorder the terms: 0.6232686977 + 1.578947368t + t2 = 340.1052632 + 0.6232686977 Combine like terms: 340.1052632 + 0.6232686977 = 340.7285318977 0.6232686977 + 1.578947368t + t2 = 340.7285318977 Factor a perfect square on the left side: (t + 0.789473684)(t + 0.789473684) = 340.7285318977 Calculate the square root of the right side: 18.458833438 Break this problem into two subproblems by setting (t + 0.789473684) equal to 18.458833438 and -18.458833438.Subproblem 1
t + 0.789473684 = 18.458833438 Simplifying t + 0.789473684 = 18.458833438 Reorder the terms: 0.789473684 + t = 18.458833438 Solving 0.789473684 + t = 18.458833438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.789473684' to each side of the equation. 0.789473684 + -0.789473684 + t = 18.458833438 + -0.789473684 Combine like terms: 0.789473684 + -0.789473684 = 0.000000000 0.000000000 + t = 18.458833438 + -0.789473684 t = 18.458833438 + -0.789473684 Combine like terms: 18.458833438 + -0.789473684 = 17.669359754 t = 17.669359754 Simplifying t = 17.669359754Subproblem 2
t + 0.789473684 = -18.458833438 Simplifying t + 0.789473684 = -18.458833438 Reorder the terms: 0.789473684 + t = -18.458833438 Solving 0.789473684 + t = -18.458833438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.789473684' to each side of the equation. 0.789473684 + -0.789473684 + t = -18.458833438 + -0.789473684 Combine like terms: 0.789473684 + -0.789473684 = 0.000000000 0.000000000 + t = -18.458833438 + -0.789473684 t = -18.458833438 + -0.789473684 Combine like terms: -18.458833438 + -0.789473684 = -19.248307122 t = -19.248307122 Simplifying t = -19.248307122Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.669359754, -19.248307122}
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