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Simplifying 4.9t2 + -2.81t + -0.26 = 0 Reorder the terms: -0.26 + -2.81t + 4.9t2 = 0 Solving -0.26 + -2.81t + 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 + -0.5734693878t + t2 = 0 Move the constant term to the right: Add '0.05306122449' to each side of the equation. -0.05306122449 + -0.5734693878t + 0.05306122449 + t2 = 0 + 0.05306122449 Reorder the terms: -0.05306122449 + 0.05306122449 + -0.5734693878t + t2 = 0 + 0.05306122449 Combine like terms: -0.05306122449 + 0.05306122449 = 0.00000000000 0.00000000000 + -0.5734693878t + t2 = 0 + 0.05306122449 -0.5734693878t + t2 = 0 + 0.05306122449 Combine like terms: 0 + 0.05306122449 = 0.05306122449 -0.5734693878t + t2 = 0.05306122449 The t term is -0.5734693878t. Take half its coefficient (-0.2867346939). Square it (0.08221678469) and add it to both sides. Add '0.08221678469' to each side of the equation. -0.5734693878t + 0.08221678469 + t2 = 0.05306122449 + 0.08221678469 Reorder the terms: 0.08221678469 + -0.5734693878t + t2 = 0.05306122449 + 0.08221678469 Combine like terms: 0.05306122449 + 0.08221678469 = 0.13527800918 0.08221678469 + -0.5734693878t + t2 = 0.13527800918 Factor a perfect square on the left side: (t + -0.2867346939)(t + -0.2867346939) = 0.13527800918 Calculate the square root of the right side: 0.367801589 Break this problem into two subproblems by setting (t + -0.2867346939) equal to 0.367801589 and -0.367801589.Subproblem 1
t + -0.2867346939 = 0.367801589 Simplifying t + -0.2867346939 = 0.367801589 Reorder the terms: -0.2867346939 + t = 0.367801589 Solving -0.2867346939 + t = 0.367801589 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2867346939' to each side of the equation. -0.2867346939 + 0.2867346939 + t = 0.367801589 + 0.2867346939 Combine like terms: -0.2867346939 + 0.2867346939 = 0.0000000000 0.0000000000 + t = 0.367801589 + 0.2867346939 t = 0.367801589 + 0.2867346939 Combine like terms: 0.367801589 + 0.2867346939 = 0.6545362829 t = 0.6545362829 Simplifying t = 0.6545362829Subproblem 2
t + -0.2867346939 = -0.367801589 Simplifying t + -0.2867346939 = -0.367801589 Reorder the terms: -0.2867346939 + t = -0.367801589 Solving -0.2867346939 + t = -0.367801589 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2867346939' to each side of the equation. -0.2867346939 + 0.2867346939 + t = -0.367801589 + 0.2867346939 Combine like terms: -0.2867346939 + 0.2867346939 = 0.0000000000 0.0000000000 + t = -0.367801589 + 0.2867346939 t = -0.367801589 + 0.2867346939 Combine like terms: -0.367801589 + 0.2867346939 = -0.0810668951 t = -0.0810668951 Simplifying t = -0.0810668951Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6545362829, -0.0810668951}
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