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Simplifying 4t2 + -8t + 3.6 = 0 Reorder the terms: 3.6 + -8t + 4t2 = 0 Solving 3.6 + -8t + 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'. 0.9 + -2t + t2 = 0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + -2t + -0.9 + t2 = 0 + -0.9 Reorder the terms: 0.9 + -0.9 + -2t + t2 = 0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + -2t + t2 = 0 + -0.9 -2t + t2 = 0 + -0.9 Combine like terms: 0 + -0.9 = -0.9 -2t + t2 = -0.9 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -0.9 + 1 Reorder the terms: 1 + -2t + t2 = -0.9 + 1 Combine like terms: -0.9 + 1 = 0.1 1 + -2t + t2 = 0.1 Factor a perfect square on the left side: (t + -1)(t + -1) = 0.1 Calculate the square root of the right side: 0.316227766 Break this problem into two subproblems by setting (t + -1) equal to 0.316227766 and -0.316227766.Subproblem 1
t + -1 = 0.316227766 Simplifying t + -1 = 0.316227766 Reorder the terms: -1 + t = 0.316227766 Solving -1 + t = 0.316227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 0.316227766 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0.316227766 + 1 t = 0.316227766 + 1 Combine like terms: 0.316227766 + 1 = 1.316227766 t = 1.316227766 Simplifying t = 1.316227766Subproblem 2
t + -1 = -0.316227766 Simplifying t + -1 = -0.316227766 Reorder the terms: -1 + t = -0.316227766 Solving -1 + t = -0.316227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -0.316227766 + 1 Combine like terms: -1 + 1 = 0 0 + t = -0.316227766 + 1 t = -0.316227766 + 1 Combine like terms: -0.316227766 + 1 = 0.683772234 t = 0.683772234 Simplifying t = 0.683772234Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.316227766, 0.683772234}
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