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Simplifying 4.9x2 + 2x + -40 = 0 Reorder the terms: -40 + 2x + 4.9x2 = 0 Solving -40 + 2x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -8.163265306 + 0.4081632653x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + 0.4081632653x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + 0.4081632653x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + 0.4081632653x + x2 = 0 + 8.163265306 0.4081632653x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 0.4081632653x + x2 = 8.163265306 The x term is 0.4081632653x. 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. 0.4081632653x + 0.04164931281 + x2 = 8.163265306 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653x + x2 = 8.163265306 + 0.04164931281 Combine like terms: 8.163265306 + 0.04164931281 = 8.20491461881 0.04164931281 + 0.4081632653x + x2 = 8.20491461881 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 8.20491461881 Calculate the square root of the right side: 2.864422214 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 2.864422214 and -2.864422214.Subproblem 1
x + 0.2040816327 = 2.864422214 Simplifying x + 0.2040816327 = 2.864422214 Reorder the terms: 0.2040816327 + x = 2.864422214 Solving 0.2040816327 + x = 2.864422214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = 2.864422214 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 2.864422214 + -0.2040816327 x = 2.864422214 + -0.2040816327 Combine like terms: 2.864422214 + -0.2040816327 = 2.6603405813 x = 2.6603405813 Simplifying x = 2.6603405813Subproblem 2
x + 0.2040816327 = -2.864422214 Simplifying x + 0.2040816327 = -2.864422214 Reorder the terms: 0.2040816327 + x = -2.864422214 Solving 0.2040816327 + x = -2.864422214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = -2.864422214 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -2.864422214 + -0.2040816327 x = -2.864422214 + -0.2040816327 Combine like terms: -2.864422214 + -0.2040816327 = -3.0685038467 x = -3.0685038467 Simplifying x = -3.0685038467Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6603405813, -3.0685038467}
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