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Simplifying 4.9t2 + -2.5t + -3 = 0 Reorder the terms: -3 + -2.5t + 4.9t2 = 0 Solving -3 + -2.5t + 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 + -0.5102040816t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -0.5102040816t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -0.5102040816t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -0.5102040816t + t2 = 0 + 0.612244898 -0.5102040816t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -0.5102040816t + t2 = 0.612244898 The t term is -0.5102040816t. Take half its coefficient (-0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. -0.5102040816t + 0.06507705122 + t2 = 0.612244898 + 0.06507705122 Reorder the terms: 0.06507705122 + -0.5102040816t + t2 = 0.612244898 + 0.06507705122 Combine like terms: 0.612244898 + 0.06507705122 = 0.67732194922 0.06507705122 + -0.5102040816t + t2 = 0.67732194922 Factor a perfect square on the left side: (t + -0.2551020408)(t + -0.2551020408) = 0.67732194922 Calculate the square root of the right side: 0.822995716 Break this problem into two subproblems by setting (t + -0.2551020408) equal to 0.822995716 and -0.822995716.Subproblem 1
t + -0.2551020408 = 0.822995716 Simplifying t + -0.2551020408 = 0.822995716 Reorder the terms: -0.2551020408 + t = 0.822995716 Solving -0.2551020408 + t = 0.822995716 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = 0.822995716 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = 0.822995716 + 0.2551020408 t = 0.822995716 + 0.2551020408 Combine like terms: 0.822995716 + 0.2551020408 = 1.0780977568 t = 1.0780977568 Simplifying t = 1.0780977568Subproblem 2
t + -0.2551020408 = -0.822995716 Simplifying t + -0.2551020408 = -0.822995716 Reorder the terms: -0.2551020408 + t = -0.822995716 Solving -0.2551020408 + t = -0.822995716 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = -0.822995716 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = -0.822995716 + 0.2551020408 t = -0.822995716 + 0.2551020408 Combine like terms: -0.822995716 + 0.2551020408 = -0.5678936752 t = -0.5678936752 Simplifying t = -0.5678936752Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.0780977568, -0.5678936752}
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