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Simplifying 4.9t2 + 3t + -3.8 = 0 Reorder the terms: -3.8 + 3t + 4.9t2 = 0 Solving -3.8 + 3t + 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'. -0.7755102041 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '0.7755102041' to each side of the equation. -0.7755102041 + 0.612244898t + 0.7755102041 + t2 = 0 + 0.7755102041 Reorder the terms: -0.7755102041 + 0.7755102041 + 0.612244898t + t2 = 0 + 0.7755102041 Combine like terms: -0.7755102041 + 0.7755102041 = 0.0000000000 0.0000000000 + 0.612244898t + t2 = 0 + 0.7755102041 0.612244898t + t2 = 0 + 0.7755102041 Combine like terms: 0 + 0.7755102041 = 0.7755102041 0.612244898t + t2 = 0.7755102041 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 = 0.7755102041 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 0.7755102041 + 0.09371095378 Combine like terms: 0.7755102041 + 0.09371095378 = 0.86922115788 0.09371095378 + 0.612244898t + t2 = 0.86922115788 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 0.86922115788 Calculate the square root of the right side: 0.932320309 Break this problem into two subproblems by setting (t + 0.306122449) equal to 0.932320309 and -0.932320309.Subproblem 1
t + 0.306122449 = 0.932320309 Simplifying t + 0.306122449 = 0.932320309 Reorder the terms: 0.306122449 + t = 0.932320309 Solving 0.306122449 + t = 0.932320309 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 = 0.932320309 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 0.932320309 + -0.306122449 t = 0.932320309 + -0.306122449 Combine like terms: 0.932320309 + -0.306122449 = 0.62619786 t = 0.62619786 Simplifying t = 0.62619786Subproblem 2
t + 0.306122449 = -0.932320309 Simplifying t + 0.306122449 = -0.932320309 Reorder the terms: 0.306122449 + t = -0.932320309 Solving 0.306122449 + t = -0.932320309 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 = -0.932320309 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -0.932320309 + -0.306122449 t = -0.932320309 + -0.306122449 Combine like terms: -0.932320309 + -0.306122449 = -1.238442758 t = -1.238442758 Simplifying t = -1.238442758Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.62619786, -1.238442758}
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