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Simplifying 2x2 + 2x + -23 = 0 Reorder the terms: -23 + 2x + 2x2 = 0 Solving -23 + 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'. -11.5 + x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x + x2 = 0 + 11.5 x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 x + x2 = 11.5 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 = 11.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 11.5 + 0.25 Combine like terms: 11.5 + 0.25 = 11.75 1.25 + 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 = 2.9278273 x = 2.9278273 Simplifying x = 2.9278273Subproblem 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 = -3.9278273 x = -3.9278273 Simplifying x = -3.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9278273, -3.9278273}
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