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Simplifying 0 = -6.1t2 + 30t + 6 Reorder the terms: 0 = 6 + 30t + -6.1t2 Solving 0 = 6 + 30t + -6.1t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -30t + 6.1t2 = 6 + 30t + -6.1t2 + -6 + -30t + 6.1t2 Reorder the terms: -6 + -30t + 6.1t2 = 6 + -6 + 30t + -30t + -6.1t2 + 6.1t2 Combine like terms: 6 + -6 = 0 -6 + -30t + 6.1t2 = 0 + 30t + -30t + -6.1t2 + 6.1t2 -6 + -30t + 6.1t2 = 30t + -30t + -6.1t2 + 6.1t2 Combine like terms: 30t + -30t = 0 -6 + -30t + 6.1t2 = 0 + -6.1t2 + 6.1t2 -6 + -30t + 6.1t2 = -6.1t2 + 6.1t2 Combine like terms: -6.1t2 + 6.1t2 = 0.0 -6 + -30t + 6.1t2 = 0.0 Begin completing the square. Divide all terms by 6.1 the coefficient of the squared term: Divide each side by '6.1'. -0.9836065574 + -4.918032787t + t2 = 0 Move the constant term to the right: Add '0.9836065574' to each side of the equation. -0.9836065574 + -4.918032787t + 0.9836065574 + t2 = 0 + 0.9836065574 Reorder the terms: -0.9836065574 + 0.9836065574 + -4.918032787t + t2 = 0 + 0.9836065574 Combine like terms: -0.9836065574 + 0.9836065574 = 0.0000000000 0.0000000000 + -4.918032787t + t2 = 0 + 0.9836065574 -4.918032787t + t2 = 0 + 0.9836065574 Combine like terms: 0 + 0.9836065574 = 0.9836065574 -4.918032787t + t2 = 0.9836065574 The t term is -4.918032787t. Take half its coefficient (-2.459016394). Square it (6.046761626) and add it to both sides. Add '6.046761626' to each side of the equation. -4.918032787t + 6.046761626 + t2 = 0.9836065574 + 6.046761626 Reorder the terms: 6.046761626 + -4.918032787t + t2 = 0.9836065574 + 6.046761626 Combine like terms: 0.9836065574 + 6.046761626 = 7.0303681834 6.046761626 + -4.918032787t + t2 = 7.0303681834 Factor a perfect square on the left side: (t + -2.459016394)(t + -2.459016394) = 7.0303681834 Calculate the square root of the right side: 2.651484147 Break this problem into two subproblems by setting (t + -2.459016394) equal to 2.651484147 and -2.651484147.Subproblem 1
t + -2.459016394 = 2.651484147 Simplifying t + -2.459016394 = 2.651484147 Reorder the terms: -2.459016394 + t = 2.651484147 Solving -2.459016394 + t = 2.651484147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.459016394' to each side of the equation. -2.459016394 + 2.459016394 + t = 2.651484147 + 2.459016394 Combine like terms: -2.459016394 + 2.459016394 = 0.000000000 0.000000000 + t = 2.651484147 + 2.459016394 t = 2.651484147 + 2.459016394 Combine like terms: 2.651484147 + 2.459016394 = 5.110500541 t = 5.110500541 Simplifying t = 5.110500541Subproblem 2
t + -2.459016394 = -2.651484147 Simplifying t + -2.459016394 = -2.651484147 Reorder the terms: -2.459016394 + t = -2.651484147 Solving -2.459016394 + t = -2.651484147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.459016394' to each side of the equation. -2.459016394 + 2.459016394 + t = -2.651484147 + 2.459016394 Combine like terms: -2.459016394 + 2.459016394 = 0.000000000 0.000000000 + t = -2.651484147 + 2.459016394 t = -2.651484147 + 2.459016394 Combine like terms: -2.651484147 + 2.459016394 = -0.192467753 t = -0.192467753 Simplifying t = -0.192467753Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.110500541, -0.192467753}
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