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Simplifying 0 = -14.5t2 + 30t + 6 Reorder the terms: 0 = 6 + 30t + -14.5t2 Solving 0 = 6 + 30t + -14.5t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -30t + 14.5t2 = 6 + 30t + -14.5t2 + -6 + -30t + 14.5t2 Reorder the terms: -6 + -30t + 14.5t2 = 6 + -6 + 30t + -30t + -14.5t2 + 14.5t2 Combine like terms: 6 + -6 = 0 -6 + -30t + 14.5t2 = 0 + 30t + -30t + -14.5t2 + 14.5t2 -6 + -30t + 14.5t2 = 30t + -30t + -14.5t2 + 14.5t2 Combine like terms: 30t + -30t = 0 -6 + -30t + 14.5t2 = 0 + -14.5t2 + 14.5t2 -6 + -30t + 14.5t2 = -14.5t2 + 14.5t2 Combine like terms: -14.5t2 + 14.5t2 = 0.0 -6 + -30t + 14.5t2 = 0.0 Begin completing the square. Divide all terms by 14.5 the coefficient of the squared term: Divide each side by '14.5'. -0.4137931034 + -2.068965517t + t2 = 0 Move the constant term to the right: Add '0.4137931034' to each side of the equation. -0.4137931034 + -2.068965517t + 0.4137931034 + t2 = 0 + 0.4137931034 Reorder the terms: -0.4137931034 + 0.4137931034 + -2.068965517t + t2 = 0 + 0.4137931034 Combine like terms: -0.4137931034 + 0.4137931034 = 0.0000000000 0.0000000000 + -2.068965517t + t2 = 0 + 0.4137931034 -2.068965517t + t2 = 0 + 0.4137931034 Combine like terms: 0 + 0.4137931034 = 0.4137931034 -2.068965517t + t2 = 0.4137931034 The t term is -2.068965517t. Take half its coefficient (-1.034482759). Square it (1.070154579) and add it to both sides. Add '1.070154579' to each side of the equation. -2.068965517t + 1.070154579 + t2 = 0.4137931034 + 1.070154579 Reorder the terms: 1.070154579 + -2.068965517t + t2 = 0.4137931034 + 1.070154579 Combine like terms: 0.4137931034 + 1.070154579 = 1.4839476824 1.070154579 + -2.068965517t + t2 = 1.4839476824 Factor a perfect square on the left side: (t + -1.034482759)(t + -1.034482759) = 1.4839476824 Calculate the square root of the right side: 1.218173913 Break this problem into two subproblems by setting (t + -1.034482759) equal to 1.218173913 and -1.218173913.Subproblem 1
t + -1.034482759 = 1.218173913 Simplifying t + -1.034482759 = 1.218173913 Reorder the terms: -1.034482759 + t = 1.218173913 Solving -1.034482759 + t = 1.218173913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.034482759' to each side of the equation. -1.034482759 + 1.034482759 + t = 1.218173913 + 1.034482759 Combine like terms: -1.034482759 + 1.034482759 = 0.000000000 0.000000000 + t = 1.218173913 + 1.034482759 t = 1.218173913 + 1.034482759 Combine like terms: 1.218173913 + 1.034482759 = 2.252656672 t = 2.252656672 Simplifying t = 2.252656672Subproblem 2
t + -1.034482759 = -1.218173913 Simplifying t + -1.034482759 = -1.218173913 Reorder the terms: -1.034482759 + t = -1.218173913 Solving -1.034482759 + t = -1.218173913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.034482759' to each side of the equation. -1.034482759 + 1.034482759 + t = -1.218173913 + 1.034482759 Combine like terms: -1.034482759 + 1.034482759 = 0.000000000 0.000000000 + t = -1.218173913 + 1.034482759 t = -1.218173913 + 1.034482759 Combine like terms: -1.218173913 + 1.034482759 = -0.183691154 t = -0.183691154 Simplifying t = -0.183691154Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.252656672, -0.183691154}
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