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Simplifying t = -16t2 + 2704 Reorder the terms: t = 2704 + -16t2 Solving t = 2704 + -16t2 Solving for variable 't'. Reorder the terms: -2704 + t + 16t2 = 2704 + -16t2 + -2704 + 16t2 Reorder the terms: -2704 + t + 16t2 = 2704 + -2704 + -16t2 + 16t2 Combine like terms: 2704 + -2704 = 0 -2704 + t + 16t2 = 0 + -16t2 + 16t2 -2704 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2704 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -169 + 0.0625t + t2 = 0 Move the constant term to the right: Add '169' to each side of the equation. -169 + 0.0625t + 169 + t2 = 0 + 169 Reorder the terms: -169 + 169 + 0.0625t + t2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 0.0625t + t2 = 0 + 169 0.0625t + t2 = 0 + 169 Combine like terms: 0 + 169 = 169 0.0625t + t2 = 169 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625t + 0.25 + t2 = 169 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 169 + 0.25 Combine like terms: 169 + 0.25 = 169.25 0.25 + 0.0625t + t2 = 169.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 169.25 Calculate the square root of the right side: 13.009611831 Break this problem into two subproblems by setting (t + 0.5) equal to 13.009611831 and -13.009611831.Subproblem 1
t + 0.5 = 13.009611831 Simplifying t + 0.5 = 13.009611831 Reorder the terms: 0.5 + t = 13.009611831 Solving 0.5 + t = 13.009611831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 13.009611831 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 13.009611831 + -0.5 t = 13.009611831 + -0.5 Combine like terms: 13.009611831 + -0.5 = 12.509611831 t = 12.509611831 Simplifying t = 12.509611831Subproblem 2
t + 0.5 = -13.009611831 Simplifying t + 0.5 = -13.009611831 Reorder the terms: 0.5 + t = -13.009611831 Solving 0.5 + t = -13.009611831 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -13.009611831 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -13.009611831 + -0.5 t = -13.009611831 + -0.5 Combine like terms: -13.009611831 + -0.5 = -13.509611831 t = -13.509611831 Simplifying t = -13.509611831Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.509611831, -13.509611831}
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