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Simplifying 2x2 + 2x + -419 = 0 Reorder the terms: -419 + 2x + 2x2 = 0 Solving -419 + 2x + 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'. -209.5 + x + x2 = 0 Move the constant term to the right: Add '209.5' to each side of the equation. -209.5 + x + 209.5 + x2 = 0 + 209.5 Reorder the terms: -209.5 + 209.5 + x + x2 = 0 + 209.5 Combine like terms: -209.5 + 209.5 = 0.0 0.0 + x + x2 = 0 + 209.5 x + x2 = 0 + 209.5 Combine like terms: 0 + 209.5 = 209.5 x + x2 = 209.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 209.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 209.5 + 0.25 Combine like terms: 209.5 + 0.25 = 209.75 1.25 + x2 = 209.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 209.75 Calculate the square root of the right side: 14.482748358 Break this problem into two subproblems by setting (x + 0.5) equal to 14.482748358 and -14.482748358.Subproblem 1
x + 0.5 = 14.482748358 Simplifying x + 0.5 = 14.482748358 Reorder the terms: 0.5 + x = 14.482748358 Solving 0.5 + x = 14.482748358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.482748358 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.482748358 + -0.5 x = 14.482748358 + -0.5 Combine like terms: 14.482748358 + -0.5 = 13.982748358 x = 13.982748358 Simplifying x = 13.982748358Subproblem 2
x + 0.5 = -14.482748358 Simplifying x + 0.5 = -14.482748358 Reorder the terms: 0.5 + x = -14.482748358 Solving 0.5 + x = -14.482748358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.482748358 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.482748358 + -0.5 x = -14.482748358 + -0.5 Combine like terms: -14.482748358 + -0.5 = -14.982748358 x = -14.982748358 Simplifying x = -14.982748358Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.982748358, -14.982748358}
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