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Simplifying 4.29t2 + -4.29t + 0.65 = 0 Reorder the terms: 0.65 + -4.29t + 4.29t2 = 0 Solving 0.65 + -4.29t + 4.29t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.29 the coefficient of the squared term: Divide each side by '4.29'. 0.1515151515 + -1t + t2 = 0 Move the constant term to the right: Add '-0.1515151515' to each side of the equation. 0.1515151515 + -1t + -0.1515151515 + t2 = 0 + -0.1515151515 Reorder the terms: 0.1515151515 + -0.1515151515 + -1t + t2 = 0 + -0.1515151515 Combine like terms: 0.1515151515 + -0.1515151515 = 0.0000000000 0.0000000000 + -1t + t2 = 0 + -0.1515151515 -1t + t2 = 0 + -0.1515151515 Combine like terms: 0 + -0.1515151515 = -0.1515151515 -1t + t2 = -0.1515151515 The t term is -1t. 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. -1t + 0.25 + t2 = -0.1515151515 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.1515151515 + 0.25 Combine like terms: -0.1515151515 + 0.25 = 0.0984848485 0.25 + -1t + t2 = 0.0984848485 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.0984848485 Calculate the square root of the right side: 0.313822957 Break this problem into two subproblems by setting (t + -0.5) equal to 0.313822957 and -0.313822957.Subproblem 1
t + -0.5 = 0.313822957 Simplifying t + -0.5 = 0.313822957 Reorder the terms: -0.5 + t = 0.313822957 Solving -0.5 + t = 0.313822957 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 = 0.313822957 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.313822957 + 0.5 t = 0.313822957 + 0.5 Combine like terms: 0.313822957 + 0.5 = 0.813822957 t = 0.813822957 Simplifying t = 0.813822957Subproblem 2
t + -0.5 = -0.313822957 Simplifying t + -0.5 = -0.313822957 Reorder the terms: -0.5 + t = -0.313822957 Solving -0.5 + t = -0.313822957 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 = -0.313822957 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.313822957 + 0.5 t = -0.313822957 + 0.5 Combine like terms: -0.313822957 + 0.5 = 0.186177043 t = 0.186177043 Simplifying t = 0.186177043Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.813822957, 0.186177043}
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