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Simplifying 2x2 + 2x + -243 = 0 Reorder the terms: -243 + 2x + 2x2 = 0 Solving -243 + 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'. -121.5 + x + x2 = 0 Move the constant term to the right: Add '121.5' to each side of the equation. -121.5 + x + 121.5 + x2 = 0 + 121.5 Reorder the terms: -121.5 + 121.5 + x + x2 = 0 + 121.5 Combine like terms: -121.5 + 121.5 = 0.0 0.0 + x + x2 = 0 + 121.5 x + x2 = 0 + 121.5 Combine like terms: 0 + 121.5 = 121.5 x + x2 = 121.5 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 = 121.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 121.5 + 0.25 Combine like terms: 121.5 + 0.25 = 121.75 1.25 + x2 = 121.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 121.75 Calculate the square root of the right side: 11.034038245 Break this problem into two subproblems by setting (x + 0.5) equal to 11.034038245 and -11.034038245.Subproblem 1
x + 0.5 = 11.034038245 Simplifying x + 0.5 = 11.034038245 Reorder the terms: 0.5 + x = 11.034038245 Solving 0.5 + x = 11.034038245 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 = 11.034038245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.034038245 + -0.5 x = 11.034038245 + -0.5 Combine like terms: 11.034038245 + -0.5 = 10.534038245 x = 10.534038245 Simplifying x = 10.534038245Subproblem 2
x + 0.5 = -11.034038245 Simplifying x + 0.5 = -11.034038245 Reorder the terms: 0.5 + x = -11.034038245 Solving 0.5 + x = -11.034038245 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 = -11.034038245 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.034038245 + -0.5 x = -11.034038245 + -0.5 Combine like terms: -11.034038245 + -0.5 = -11.534038245 x = -11.534038245 Simplifying x = -11.534038245Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.534038245, -11.534038245}
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