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Simplifying 0 = t2 + -8t + -0.25 Reorder the terms: 0 = -0.25 + -8t + t2 Solving 0 = -0.25 + -8t + t2 Solving for variable 't'. Combine like terms: 0 + 0.25 = 0.25 0.25 + 8t + -1t2 = -0.25 + -8t + t2 + 0.25 + 8t + -1t2 Reorder the terms: 0.25 + 8t + -1t2 = -0.25 + 0.25 + -8t + 8t + t2 + -1t2 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + 8t + -1t2 = 0.00 + -8t + 8t + t2 + -1t2 0.25 + 8t + -1t2 = -8t + 8t + t2 + -1t2 Combine like terms: -8t + 8t = 0 0.25 + 8t + -1t2 = 0 + t2 + -1t2 0.25 + 8t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 0.25 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.25 + -8t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -8t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -8t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -8t + t2 = 0 + 0.25 -8t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -8t + t2 = 0.25 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 0.25 + 16 Reorder the terms: 16 + -8t + t2 = 0.25 + 16 Combine like terms: 0.25 + 16 = 16.25 16 + -8t + t2 = 16.25 Factor a perfect square on the left side: (t + -4)(t + -4) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (t + -4) equal to 4.031128874 and -4.031128874.Subproblem 1
t + -4 = 4.031128874 Simplifying t + -4 = 4.031128874 Reorder the terms: -4 + t = 4.031128874 Solving -4 + t = 4.031128874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.031128874 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.031128874 + 4 t = 4.031128874 + 4 Combine like terms: 4.031128874 + 4 = 8.031128874 t = 8.031128874 Simplifying t = 8.031128874Subproblem 2
t + -4 = -4.031128874 Simplifying t + -4 = -4.031128874 Reorder the terms: -4 + t = -4.031128874 Solving -4 + t = -4.031128874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.031128874 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.031128874 + 4 t = -4.031128874 + 4 Combine like terms: -4.031128874 + 4 = -0.031128874 t = -0.031128874 Simplifying t = -0.031128874Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.031128874, -0.031128874}
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