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Simplifying x + 2x2 + -416 = 0 Reorder the terms: -416 + x + 2x2 = 0 Solving -416 + x + 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'. -208 + 0.5x + x2 = 0 Move the constant term to the right: Add '208' to each side of the equation. -208 + 0.5x + 208 + x2 = 0 + 208 Reorder the terms: -208 + 208 + 0.5x + x2 = 0 + 208 Combine like terms: -208 + 208 = 0 0 + 0.5x + x2 = 0 + 208 0.5x + x2 = 0 + 208 Combine like terms: 0 + 208 = 208 0.5x + x2 = 208 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. 0.5x + 0.25 + x2 = 208 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 208 + 0.25 Combine like terms: 208 + 0.25 = 208.25 0.25 + 0.5x + x2 = 208.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (x + 0.5) equal to 14.43086969 and -14.43086969.Subproblem 1
x + 0.5 = 14.43086969 Simplifying x + 0.5 = 14.43086969 Reorder the terms: 0.5 + x = 14.43086969 Solving 0.5 + x = 14.43086969 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 = 14.43086969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.43086969 + -0.5 x = 14.43086969 + -0.5 Combine like terms: 14.43086969 + -0.5 = 13.93086969 x = 13.93086969 Simplifying x = 13.93086969Subproblem 2
x + 0.5 = -14.43086969 Simplifying x + 0.5 = -14.43086969 Reorder the terms: 0.5 + x = -14.43086969 Solving 0.5 + x = -14.43086969 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 = -14.43086969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.43086969 + -0.5 x = -14.43086969 + -0.5 Combine like terms: -14.43086969 + -0.5 = -14.93086969 x = -14.93086969 Simplifying x = -14.93086969Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.93086969, -14.93086969}
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