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Simplifying 2x2 + -2x = 23 Reorder the terms: -2x + 2x2 = 23 Solving -2x + 2x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -2x + 2x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -1x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -1x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -1x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -1x + x2 = 0 + 11.5 -1x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -1x + x2 = 11.5 The x term is -1x. 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. -1x + 0.25 + x2 = 11.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11.5 + 0.25 Combine like terms: 11.5 + 0.25 = 11.75 0.25 + -1x + x2 = 11.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + -0.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + -0.5 = 3.4278273 Simplifying x + -0.5 = 3.4278273 Reorder the terms: -0.5 + x = 3.4278273 Solving -0.5 + x = 3.4278273 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 = 3.4278273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.4278273 + 0.5 x = 3.4278273 + 0.5 Combine like terms: 3.4278273 + 0.5 = 3.9278273 x = 3.9278273 Simplifying x = 3.9278273Subproblem 2
x + -0.5 = -3.4278273 Simplifying x + -0.5 = -3.4278273 Reorder the terms: -0.5 + x = -3.4278273 Solving -0.5 + x = -3.4278273 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 = -3.4278273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.4278273 + 0.5 x = -3.4278273 + 0.5 Combine like terms: -3.4278273 + 0.5 = -2.9278273 x = -2.9278273 Simplifying x = -2.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9278273, -2.9278273}
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