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Simplifying (-1x2) + x + 23 = 0 Reorder the terms: 23 + x + (-1x2) = 0 Solving 23 + x + (-1x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + -1x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -1x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -1x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x + x2 = 0 + 23 -1x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -1x + x2 = 23 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. -1x + 0.25 + x2 = 23 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 23 + 0.25 Combine like terms: 23 + 0.25 = 23.25 0.25 + -1x + x2 = 23.25 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting ((x) + 0.5) equal to 4.82182538 and -4.82182538.Subproblem 1
(x) + 0.5 = 4.82182538 Simplifying (x) + 0.5 = 4.82182538 x + 0.5 = 4.82182538 Reorder the terms: 0.5 + x = 4.82182538 Solving 0.5 + x = 4.82182538 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 = 4.82182538 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.82182538 + -0.5 x = 4.82182538 + -0.5 Combine like terms: 4.82182538 + -0.5 = 4.32182538 x = 4.32182538 Simplifying x = 4.32182538Subproblem 2
(x) + 0.5 = -4.82182538 Simplifying (x) + 0.5 = -4.82182538 x + 0.5 = -4.82182538 Reorder the terms: 0.5 + x = -4.82182538 Solving 0.5 + x = -4.82182538 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 = -4.82182538 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.82182538 + -0.5 x = -4.82182538 + -0.5 Combine like terms: -4.82182538 + -0.5 = -5.32182538 x = -5.32182538 Simplifying x = -5.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.32182538, -5.32182538}
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