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Simplifying 4.9t2 + 2.5t + -50 = 0 Reorder the terms: -50 + 2.5t + 4.9t2 = 0 Solving -50 + 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'. -10.20408163 + 0.5102040816t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.5102040816t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.5102040816t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.5102040816t + t2 = 0 + 10.20408163 0.5102040816t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.5102040816t + t2 = 10.20408163 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 = 10.20408163 + 0.06507705122 Reorder the terms: 0.06507705122 + 0.5102040816t + t2 = 10.20408163 + 0.06507705122 Combine like terms: 10.20408163 + 0.06507705122 = 10.26915868122 0.06507705122 + 0.5102040816t + t2 = 10.26915868122 Factor a perfect square on the left side: (t + 0.2551020408)(t + 0.2551020408) = 10.26915868122 Calculate the square root of the right side: 3.204552805 Break this problem into two subproblems by setting (t + 0.2551020408) equal to 3.204552805 and -3.204552805.Subproblem 1
t + 0.2551020408 = 3.204552805 Simplifying t + 0.2551020408 = 3.204552805 Reorder the terms: 0.2551020408 + t = 3.204552805 Solving 0.2551020408 + t = 3.204552805 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 = 3.204552805 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = 3.204552805 + -0.2551020408 t = 3.204552805 + -0.2551020408 Combine like terms: 3.204552805 + -0.2551020408 = 2.9494507642 t = 2.9494507642 Simplifying t = 2.9494507642Subproblem 2
t + 0.2551020408 = -3.204552805 Simplifying t + 0.2551020408 = -3.204552805 Reorder the terms: 0.2551020408 + t = -3.204552805 Solving 0.2551020408 + t = -3.204552805 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 = -3.204552805 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + t = -3.204552805 + -0.2551020408 t = -3.204552805 + -0.2551020408 Combine like terms: -3.204552805 + -0.2551020408 = -3.4596548458 t = -3.4596548458 Simplifying t = -3.4596548458Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.9494507642, -3.4596548458}
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