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Simplifying 4.9t2 + 3t = 5.2 Reorder the terms: 3t + 4.9t2 = 5.2 Solving 3t + 4.9t2 = 5.2 Solving for variable 't'. Reorder the terms: -5.2 + 3t + 4.9t2 = 5.2 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 -5.2 + 3t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.06122449 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '1.06122449' to each side of the equation. -1.06122449 + 0.612244898t + 1.06122449 + t2 = 0 + 1.06122449 Reorder the terms: -1.06122449 + 1.06122449 + 0.612244898t + t2 = 0 + 1.06122449 Combine like terms: -1.06122449 + 1.06122449 = 0.00000000 0.00000000 + 0.612244898t + t2 = 0 + 1.06122449 0.612244898t + t2 = 0 + 1.06122449 Combine like terms: 0 + 1.06122449 = 1.06122449 0.612244898t + t2 = 1.06122449 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 1.06122449 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 1.06122449 + 0.09371095378 Combine like terms: 1.06122449 + 0.09371095378 = 1.15493544378 0.09371095378 + 0.612244898t + t2 = 1.15493544378 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 1.15493544378 Calculate the square root of the right side: 1.074679228 Break this problem into two subproblems by setting (t + 0.306122449) equal to 1.074679228 and -1.074679228.Subproblem 1
t + 0.306122449 = 1.074679228 Simplifying t + 0.306122449 = 1.074679228 Reorder the terms: 0.306122449 + t = 1.074679228 Solving 0.306122449 + t = 1.074679228 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 1.074679228 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 1.074679228 + -0.306122449 t = 1.074679228 + -0.306122449 Combine like terms: 1.074679228 + -0.306122449 = 0.768556779 t = 0.768556779 Simplifying t = 0.768556779Subproblem 2
t + 0.306122449 = -1.074679228 Simplifying t + 0.306122449 = -1.074679228 Reorder the terms: 0.306122449 + t = -1.074679228 Solving 0.306122449 + t = -1.074679228 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -1.074679228 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -1.074679228 + -0.306122449 t = -1.074679228 + -0.306122449 Combine like terms: -1.074679228 + -0.306122449 = -1.380801677 t = -1.380801677 Simplifying t = -1.380801677Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.768556779, -1.380801677}
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