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Simplifying -4.9t2 + 27t + 1 = 0 Reorder the terms: 1 + 27t + -4.9t2 = 0 Solving 1 + 27t + -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'. -0.2040816327 + -5.510204082t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -5.510204082t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -5.510204082t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -5.510204082t + t2 = 0 + 0.2040816327 -5.510204082t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -5.510204082t + t2 = 0.2040816327 The t term is -5.510204082t. Take half its coefficient (-2.755102041). Square it (7.590587256) and add it to both sides. Add '7.590587256' to each side of the equation. -5.510204082t + 7.590587256 + t2 = 0.2040816327 + 7.590587256 Reorder the terms: 7.590587256 + -5.510204082t + t2 = 0.2040816327 + 7.590587256 Combine like terms: 0.2040816327 + 7.590587256 = 7.7946688887 7.590587256 + -5.510204082t + t2 = 7.7946688887 Factor a perfect square on the left side: (t + -2.755102041)(t + -2.755102041) = 7.7946688887 Calculate the square root of the right side: 2.791893424 Break this problem into two subproblems by setting (t + -2.755102041) equal to 2.791893424 and -2.791893424.Subproblem 1
t + -2.755102041 = 2.791893424 Simplifying t + -2.755102041 = 2.791893424 Reorder the terms: -2.755102041 + t = 2.791893424 Solving -2.755102041 + t = 2.791893424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + t = 2.791893424 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + t = 2.791893424 + 2.755102041 t = 2.791893424 + 2.755102041 Combine like terms: 2.791893424 + 2.755102041 = 5.546995465 t = 5.546995465 Simplifying t = 5.546995465Subproblem 2
t + -2.755102041 = -2.791893424 Simplifying t + -2.755102041 = -2.791893424 Reorder the terms: -2.755102041 + t = -2.791893424 Solving -2.755102041 + t = -2.791893424 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.755102041' to each side of the equation. -2.755102041 + 2.755102041 + t = -2.791893424 + 2.755102041 Combine like terms: -2.755102041 + 2.755102041 = 0.000000000 0.000000000 + t = -2.791893424 + 2.755102041 t = -2.791893424 + 2.755102041 Combine like terms: -2.791893424 + 2.755102041 = -0.036791383 t = -0.036791383 Simplifying t = -0.036791383Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.546995465, -0.036791383}
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