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Simplifying t = -16t2 + 116 Reorder the terms: t = 116 + -16t2 Solving t = 116 + -16t2 Solving for variable 't'. Reorder the terms: -116 + t + 16t2 = 116 + -16t2 + -116 + 16t2 Reorder the terms: -116 + t + 16t2 = 116 + -116 + -16t2 + 16t2 Combine like terms: 116 + -116 = 0 -116 + t + 16t2 = 0 + -16t2 + 16t2 -116 + t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -116 + t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.25 + 0.0625t + t2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 0.0625t + 7.25 + t2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 0.0625t + t2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 0.0625t + t2 = 0 + 7.25 0.0625t + t2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 0.0625t + t2 = 7.25 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 = 7.25 + 0.25 Reorder the terms: 0.25 + 0.0625t + t2 = 7.25 + 0.25 Combine like terms: 7.25 + 0.25 = 7.5 0.25 + 0.0625t + t2 = 7.5 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (t + 0.5) equal to 2.738612788 and -2.738612788.Subproblem 1
t + 0.5 = 2.738612788 Simplifying t + 0.5 = 2.738612788 Reorder the terms: 0.5 + t = 2.738612788 Solving 0.5 + t = 2.738612788 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 = 2.738612788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.738612788 + -0.5 t = 2.738612788 + -0.5 Combine like terms: 2.738612788 + -0.5 = 2.238612788 t = 2.238612788 Simplifying t = 2.238612788Subproblem 2
t + 0.5 = -2.738612788 Simplifying t + 0.5 = -2.738612788 Reorder the terms: 0.5 + t = -2.738612788 Solving 0.5 + t = -2.738612788 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 = -2.738612788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.738612788 + -0.5 t = -2.738612788 + -0.5 Combine like terms: -2.738612788 + -0.5 = -3.238612788 t = -3.238612788 Simplifying t = -3.238612788Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.238612788, -3.238612788}
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