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Simplifying 0 = 8t2 + 6t + -1 Reorder the terms: 0 = -1 + 6t + 8t2 Solving 0 = -1 + 6t + 8t2 Solving for variable 't'. Combine like terms: 0 + 1 = 1 1 + -6t + -8t2 = -1 + 6t + 8t2 + 1 + -6t + -8t2 Reorder the terms: 1 + -6t + -8t2 = -1 + 1 + 6t + -6t + 8t2 + -8t2 Combine like terms: -1 + 1 = 0 1 + -6t + -8t2 = 0 + 6t + -6t + 8t2 + -8t2 1 + -6t + -8t2 = 6t + -6t + 8t2 + -8t2 Combine like terms: 6t + -6t = 0 1 + -6t + -8t2 = 0 + 8t2 + -8t2 1 + -6t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 1 + -6t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + 0.75t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.75t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.75t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.75t + t2 = 0 + 0.125 0.75t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.75t + t2 = 0.125 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 0.125 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 0.125 + 0.140625 Combine like terms: 0.125 + 0.140625 = 0.265625 0.140625 + 0.75t + t2 = 0.265625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (t + 0.375) equal to 0.515388203 and -0.515388203.Subproblem 1
t + 0.375 = 0.515388203 Simplifying t + 0.375 = 0.515388203 Reorder the terms: 0.375 + t = 0.515388203 Solving 0.375 + t = 0.515388203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 0.515388203 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 0.515388203 + -0.375 t = 0.515388203 + -0.375 Combine like terms: 0.515388203 + -0.375 = 0.140388203 t = 0.140388203 Simplifying t = 0.140388203Subproblem 2
t + 0.375 = -0.515388203 Simplifying t + 0.375 = -0.515388203 Reorder the terms: 0.375 + t = -0.515388203 Solving 0.375 + t = -0.515388203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -0.515388203 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -0.515388203 + -0.375 t = -0.515388203 + -0.375 Combine like terms: -0.515388203 + -0.375 = -0.890388203 t = -0.890388203 Simplifying t = -0.890388203Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.140388203, -0.890388203}
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