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Simplifying 8t2 + -6 + -4t + 3 = 0 Reorder the terms: -6 + 3 + -4t + 8t2 = 0 Combine like terms: -6 + 3 = -3 -3 + -4t + 8t2 = 0 Solving -3 + -4t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.5t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.5t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.5t + t2 = 0 + 0.375 -0.5t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.5t + t2 = 0.375 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 = 0.375 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.375 + 0.0625 Combine like terms: 0.375 + 0.0625 = 0.4375 0.0625 + -0.5t + t2 = 0.4375 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (t + -0.25) equal to 0.661437828 and -0.661437828.Subproblem 1
t + -0.25 = 0.661437828 Simplifying t + -0.25 = 0.661437828 Reorder the terms: -0.25 + t = 0.661437828 Solving -0.25 + t = 0.661437828 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 = 0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.661437828 + 0.25 t = 0.661437828 + 0.25 Combine like terms: 0.661437828 + 0.25 = 0.911437828 t = 0.911437828 Simplifying t = 0.911437828Subproblem 2
t + -0.25 = -0.661437828 Simplifying t + -0.25 = -0.661437828 Reorder the terms: -0.25 + t = -0.661437828 Solving -0.25 + t = -0.661437828 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 = -0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.661437828 + 0.25 t = -0.661437828 + 0.25 Combine like terms: -0.661437828 + 0.25 = -0.411437828 t = -0.411437828 Simplifying t = -0.411437828Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.911437828, -0.411437828}
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