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Simplifying 4.9t2 + 1.28t + -0.26 = 0 Reorder the terms: -0.26 + 1.28t + 4.9t2 = 0 Solving -0.26 + 1.28t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.05306122449 + 0.2612244898t + t2 = 0 Move the constant term to the right: Add '0.05306122449' to each side of the equation. -0.05306122449 + 0.2612244898t + 0.05306122449 + t2 = 0 + 0.05306122449 Reorder the terms: -0.05306122449 + 0.05306122449 + 0.2612244898t + t2 = 0 + 0.05306122449 Combine like terms: -0.05306122449 + 0.05306122449 = 0.00000000000 0.00000000000 + 0.2612244898t + t2 = 0 + 0.05306122449 0.2612244898t + t2 = 0 + 0.05306122449 Combine like terms: 0 + 0.05306122449 = 0.05306122449 0.2612244898t + t2 = 0.05306122449 The t term is 0.2612244898t. Take half its coefficient (0.1306122449). Square it (0.01705955852) and add it to both sides. Add '0.01705955852' to each side of the equation. 0.2612244898t + 0.01705955852 + t2 = 0.05306122449 + 0.01705955852 Reorder the terms: 0.01705955852 + 0.2612244898t + t2 = 0.05306122449 + 0.01705955852 Combine like terms: 0.05306122449 + 0.01705955852 = 0.07012078301 0.01705955852 + 0.2612244898t + t2 = 0.07012078301 Factor a perfect square on the left side: (t + 0.1306122449)(t + 0.1306122449) = 0.07012078301 Calculate the square root of the right side: 0.264803291 Break this problem into two subproblems by setting (t + 0.1306122449) equal to 0.264803291 and -0.264803291.Subproblem 1
t + 0.1306122449 = 0.264803291 Simplifying t + 0.1306122449 = 0.264803291 Reorder the terms: 0.1306122449 + t = 0.264803291 Solving 0.1306122449 + t = 0.264803291 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1306122449' to each side of the equation. 0.1306122449 + -0.1306122449 + t = 0.264803291 + -0.1306122449 Combine like terms: 0.1306122449 + -0.1306122449 = 0.0000000000 0.0000000000 + t = 0.264803291 + -0.1306122449 t = 0.264803291 + -0.1306122449 Combine like terms: 0.264803291 + -0.1306122449 = 0.1341910461 t = 0.1341910461 Simplifying t = 0.1341910461Subproblem 2
t + 0.1306122449 = -0.264803291 Simplifying t + 0.1306122449 = -0.264803291 Reorder the terms: 0.1306122449 + t = -0.264803291 Solving 0.1306122449 + t = -0.264803291 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1306122449' to each side of the equation. 0.1306122449 + -0.1306122449 + t = -0.264803291 + -0.1306122449 Combine like terms: 0.1306122449 + -0.1306122449 = 0.0000000000 0.0000000000 + t = -0.264803291 + -0.1306122449 t = -0.264803291 + -0.1306122449 Combine like terms: -0.264803291 + -0.1306122449 = -0.3954155359 t = -0.3954155359 Simplifying t = -0.3954155359Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.1341910461, -0.3954155359}
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