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Simplifying x2 + 23x + 81 = 0 Reorder the terms: 81 + 23x + x2 = 0 Solving 81 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 23x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + 23x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 23x + x2 = 0 + -81 23x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 23x + x2 = -81 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = -81 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -81 + 132.25 Combine like terms: -81 + 132.25 = 51.25 132.25 + 23x + x2 = 51.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 11.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 11.5 = 7.158910532 Simplifying x + 11.5 = 7.158910532 Reorder the terms: 11.5 + x = 7.158910532 Solving 11.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 7.158910532 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 7.158910532 + -11.5 x = 7.158910532 + -11.5 Combine like terms: 7.158910532 + -11.5 = -4.341089468 x = -4.341089468 Simplifying x = -4.341089468Subproblem 2
x + 11.5 = -7.158910532 Simplifying x + 11.5 = -7.158910532 Reorder the terms: 11.5 + x = -7.158910532 Solving 11.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -7.158910532 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -7.158910532 + -11.5 x = -7.158910532 + -11.5 Combine like terms: -7.158910532 + -11.5 = -18.658910532 x = -18.658910532 Simplifying x = -18.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.341089468, -18.658910532}
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