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Simplifying 4.9t2 + 9t + 3 = 0 Reorder the terms: 3 + 9t + 4.9t2 = 0 Solving 3 + 9t + 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'. 0.612244898 + 1.836734694t + t2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + 1.836734694t + -0.612244898 + t2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + 1.836734694t + t2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + 1.836734694t + t2 = 0 + -0.612244898 1.836734694t + t2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 1.836734694t + t2 = -0.612244898 The t term is 1.836734694t. Take half its coefficient (0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. 1.836734694t + 0.8433985840 + t2 = -0.612244898 + 0.8433985840 Reorder the terms: 0.8433985840 + 1.836734694t + t2 = -0.612244898 + 0.8433985840 Combine like terms: -0.612244898 + 0.8433985840 = 0.231153686 0.8433985840 + 1.836734694t + t2 = 0.231153686 Factor a perfect square on the left side: (t + 0.918367347)(t + 0.918367347) = 0.231153686 Calculate the square root of the right side: 0.480784449 Break this problem into two subproblems by setting (t + 0.918367347) equal to 0.480784449 and -0.480784449.Subproblem 1
t + 0.918367347 = 0.480784449 Simplifying t + 0.918367347 = 0.480784449 Reorder the terms: 0.918367347 + t = 0.480784449 Solving 0.918367347 + t = 0.480784449 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + t = 0.480784449 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = 0.480784449 + -0.918367347 t = 0.480784449 + -0.918367347 Combine like terms: 0.480784449 + -0.918367347 = -0.437582898 t = -0.437582898 Simplifying t = -0.437582898Subproblem 2
t + 0.918367347 = -0.480784449 Simplifying t + 0.918367347 = -0.480784449 Reorder the terms: 0.918367347 + t = -0.480784449 Solving 0.918367347 + t = -0.480784449 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.918367347' to each side of the equation. 0.918367347 + -0.918367347 + t = -0.480784449 + -0.918367347 Combine like terms: 0.918367347 + -0.918367347 = 0.000000000 0.000000000 + t = -0.480784449 + -0.918367347 t = -0.480784449 + -0.918367347 Combine like terms: -0.480784449 + -0.918367347 = -1.399151796 t = -1.399151796 Simplifying t = -1.399151796Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.437582898, -1.399151796}
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