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Simplifying 4.9x2 + 2x + -350 = 0 Reorder the terms: -350 + 2x + 4.9x2 = 0 Solving -350 + 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'. -71.42857143 + 0.4081632653x + x2 = 0 Move the constant term to the right: Add '71.42857143' to each side of the equation. -71.42857143 + 0.4081632653x + 71.42857143 + x2 = 0 + 71.42857143 Reorder the terms: -71.42857143 + 71.42857143 + 0.4081632653x + x2 = 0 + 71.42857143 Combine like terms: -71.42857143 + 71.42857143 = 0.00000000 0.00000000 + 0.4081632653x + x2 = 0 + 71.42857143 0.4081632653x + x2 = 0 + 71.42857143 Combine like terms: 0 + 71.42857143 = 71.42857143 0.4081632653x + x2 = 71.42857143 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 = 71.42857143 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653x + x2 = 71.42857143 + 0.04164931281 Combine like terms: 71.42857143 + 0.04164931281 = 71.47022074281 0.04164931281 + 0.4081632653x + x2 = 71.47022074281 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 71.47022074281 Calculate the square root of the right side: 8.454006195 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 8.454006195 and -8.454006195.Subproblem 1
x + 0.2040816327 = 8.454006195 Simplifying x + 0.2040816327 = 8.454006195 Reorder the terms: 0.2040816327 + x = 8.454006195 Solving 0.2040816327 + x = 8.454006195 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 = 8.454006195 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 8.454006195 + -0.2040816327 x = 8.454006195 + -0.2040816327 Combine like terms: 8.454006195 + -0.2040816327 = 8.2499245623 x = 8.2499245623 Simplifying x = 8.2499245623Subproblem 2
x + 0.2040816327 = -8.454006195 Simplifying x + 0.2040816327 = -8.454006195 Reorder the terms: 0.2040816327 + x = -8.454006195 Solving 0.2040816327 + x = -8.454006195 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 = -8.454006195 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -8.454006195 + -0.2040816327 x = -8.454006195 + -0.2040816327 Combine like terms: -8.454006195 + -0.2040816327 = -8.6580878277 x = -8.6580878277 Simplifying x = -8.6580878277Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.2499245623, -8.6580878277}
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