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Simplifying -16t2 + 8t + 48 = 0.25 Reorder the terms: 48 + 8t + -16t2 = 0.25 Solving 48 + 8t + -16t2 = 0.25 Solving for variable 't'. Reorder the terms: 48 + -0.25 + 8t + -16t2 = 0.25 + -0.25 Combine like terms: 48 + -0.25 = 47.75 47.75 + 8t + -16t2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 47.75 + 8t + -16t2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.984375 + -0.5t + t2 = 0.00 Move the constant term to the right: Add '2.984375' to each side of the equation. -2.984375 + -0.5t + 2.984375 + t2 = 0.00 + 2.984375 Reorder the terms: -2.984375 + 2.984375 + -0.5t + t2 = 0.00 + 2.984375 Combine like terms: -2.984375 + 2.984375 = 0.000000 0.000000 + -0.5t + t2 = 0.00 + 2.984375 -0.5t + t2 = 0.00 + 2.984375 Combine like terms: 0.00 + 2.984375 = 2.984375 -0.5t + t2 = 2.984375 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 2.984375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 2.984375 + 0.0625 Combine like terms: 2.984375 + 0.0625 = 3.046875 0.0625 + -0.5t + t2 = 3.046875 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 3.046875 Calculate the square root of the right side: 1.745530005 Break this problem into two subproblems by setting (t + -0.25) equal to 1.745530005 and -1.745530005.Subproblem 1
t + -0.25 = 1.745530005 Simplifying t + -0.25 = 1.745530005 Reorder the terms: -0.25 + t = 1.745530005 Solving -0.25 + t = 1.745530005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.745530005 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.745530005 + 0.25 t = 1.745530005 + 0.25 Combine like terms: 1.745530005 + 0.25 = 1.995530005 t = 1.995530005 Simplifying t = 1.995530005Subproblem 2
t + -0.25 = -1.745530005 Simplifying t + -0.25 = -1.745530005 Reorder the terms: -0.25 + t = -1.745530005 Solving -0.25 + t = -1.745530005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.745530005 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.745530005 + 0.25 t = -1.745530005 + 0.25 Combine like terms: -1.745530005 + 0.25 = -1.495530005 t = -1.495530005 Simplifying t = -1.495530005Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.995530005, -1.495530005}
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