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Simplifying t = -16t2 + 1050 Reorder the terms: t = 1050 + -16t2 Solving t = 1050 + -16t2 Solving for variable 't'. Reorder the terms: -1050 + t + 16t2 = 1050 + -16t2 + -1050 + 16t2 Reorder the terms: -1050 + t + 16t2 = 1050 + -1050 + -16t2 + 16t2 Combine like terms: 1050 + -1050 = 0 -1050 + t + 16t2 = 0 + -16t2 + 16t2 -1050 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1050 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -65.625 + 0.0625t + t2 = 0 Move the constant term to the right: Add '65.625' to each side of the equation. -65.625 + 0.0625t + 65.625 + t2 = 0 + 65.625 Reorder the terms: -65.625 + 65.625 + 0.0625t + t2 = 0 + 65.625 Combine like terms: -65.625 + 65.625 = 0.000 0.000 + 0.0625t + t2 = 0 + 65.625 0.0625t + t2 = 0 + 65.625 Combine like terms: 0 + 65.625 = 65.625 0.0625t + t2 = 65.625 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 = 65.625 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 65.625 + 0.25 Combine like terms: 65.625 + 0.25 = 65.875 0.25 + 0.0625t + t2 = 65.875 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 65.875 Calculate the square root of the right side: 8.11634154 Break this problem into two subproblems by setting (t + 0.5) equal to 8.11634154 and -8.11634154.Subproblem 1
t + 0.5 = 8.11634154 Simplifying t + 0.5 = 8.11634154 Reorder the terms: 0.5 + t = 8.11634154 Solving 0.5 + t = 8.11634154 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 = 8.11634154 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 8.11634154 + -0.5 t = 8.11634154 + -0.5 Combine like terms: 8.11634154 + -0.5 = 7.61634154 t = 7.61634154 Simplifying t = 7.61634154Subproblem 2
t + 0.5 = -8.11634154 Simplifying t + 0.5 = -8.11634154 Reorder the terms: 0.5 + t = -8.11634154 Solving 0.5 + t = -8.11634154 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 = -8.11634154 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -8.11634154 + -0.5 t = -8.11634154 + -0.5 Combine like terms: -8.11634154 + -0.5 = -8.61634154 t = -8.61634154 Simplifying t = -8.61634154Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.61634154, -8.61634154}
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