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Simplifying -2t + 4.9t2 = 7 Solving -2t + 4.9t2 = 7 Solving for variable 't'. Reorder the terms: -7 + -2t + 4.9t2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -2t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.428571429 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.4081632653t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.4081632653t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.4081632653t + t2 = 0 + 1.428571429 -0.4081632653t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.4081632653t + t2 = 1.428571429 The t term is -0.4081632653t. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653t + 0.04164931281 + t2 = 1.428571429 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 1.428571429 + 0.04164931281 Combine like terms: 1.428571429 + 0.04164931281 = 1.47022074181 0.04164931281 + -0.4081632653t + t2 = 1.47022074181 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 1.47022074181 Calculate the square root of the right side: 1.212526594 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 1.212526594 and -1.212526594.Subproblem 1
t + -0.2040816327 = 1.212526594 Simplifying t + -0.2040816327 = 1.212526594 Reorder the terms: -0.2040816327 + t = 1.212526594 Solving -0.2040816327 + t = 1.212526594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = 1.212526594 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 1.212526594 + 0.2040816327 t = 1.212526594 + 0.2040816327 Combine like terms: 1.212526594 + 0.2040816327 = 1.4166082267 t = 1.4166082267 Simplifying t = 1.4166082267Subproblem 2
t + -0.2040816327 = -1.212526594 Simplifying t + -0.2040816327 = -1.212526594 Reorder the terms: -0.2040816327 + t = -1.212526594 Solving -0.2040816327 + t = -1.212526594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = -1.212526594 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -1.212526594 + 0.2040816327 t = -1.212526594 + 0.2040816327 Combine like terms: -1.212526594 + 0.2040816327 = -1.0084449613 t = -1.0084449613 Simplifying t = -1.0084449613Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4166082267, -1.0084449613}
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