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Simplifying 2x2 + 3x + -246 = 0 Reorder the terms: -246 + 3x + 2x2 = 0 Solving -246 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -123 + 1.5x + x2 = 0 Move the constant term to the right: Add '123' to each side of the equation. -123 + 1.5x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 1.5x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 1.5x + x2 = 0 + 123 1.5x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 1.5x + x2 = 123 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 123 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 123 + 0.5625 Combine like terms: 123 + 0.5625 = 123.5625 0.5625 + 1.5x + x2 = 123.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 123.5625 Calculate the square root of the right side: 11.115867038 Break this problem into two subproblems by setting (x + 0.75) equal to 11.115867038 and -11.115867038.Subproblem 1
x + 0.75 = 11.115867038 Simplifying x + 0.75 = 11.115867038 Reorder the terms: 0.75 + x = 11.115867038 Solving 0.75 + x = 11.115867038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 11.115867038 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 11.115867038 + -0.75 x = 11.115867038 + -0.75 Combine like terms: 11.115867038 + -0.75 = 10.365867038 x = 10.365867038 Simplifying x = 10.365867038Subproblem 2
x + 0.75 = -11.115867038 Simplifying x + 0.75 = -11.115867038 Reorder the terms: 0.75 + x = -11.115867038 Solving 0.75 + x = -11.115867038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -11.115867038 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -11.115867038 + -0.75 x = -11.115867038 + -0.75 Combine like terms: -11.115867038 + -0.75 = -11.865867038 x = -11.865867038 Simplifying x = -11.865867038Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.365867038, -11.865867038}
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