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Simplifying 4t2 + 4t + -0.75 = 0 Reorder the terms: -0.75 + 4t + 4t2 = 0 Solving -0.75 + 4t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.1875 + t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + t + t2 = 0 + 0.1875 t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 t + t2 = 0.1875 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. + 0.25 + t2 = 0.1875 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.1875 + 0.25 Combine like terms: 0.1875 + 0.25 = 0.4375 1.25 + t2 = 0.4375 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (t + 0.5) equal to 0.661437828 and -0.661437828.Subproblem 1
t + 0.5 = 0.661437828 Simplifying t + 0.5 = 0.661437828 Reorder the terms: 0.5 + t = 0.661437828 Solving 0.5 + t = 0.661437828 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 = 0.661437828 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.661437828 + -0.5 t = 0.661437828 + -0.5 Combine like terms: 0.661437828 + -0.5 = 0.161437828 t = 0.161437828 Simplifying t = 0.161437828Subproblem 2
t + 0.5 = -0.661437828 Simplifying t + 0.5 = -0.661437828 Reorder the terms: 0.5 + t = -0.661437828 Solving 0.5 + t = -0.661437828 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 = -0.661437828 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.661437828 + -0.5 t = -0.661437828 + -0.5 Combine like terms: -0.661437828 + -0.5 = -1.161437828 t = -1.161437828 Simplifying t = -1.161437828Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.161437828, -1.161437828}
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