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Simplifying x2 + 23x + 11 = 0 Reorder the terms: 11 + 23x + x2 = 0 Solving 11 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 23x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 23x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 23x + x2 = 0 + -11 23x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 23x + x2 = -11 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 = -11 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -11 + 132.25 Combine like terms: -11 + 132.25 = 121.25 132.25 + 23x + x2 = 121.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + 11.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + 11.5 = 11.011357773 Simplifying x + 11.5 = 11.011357773 Reorder the terms: 11.5 + x = 11.011357773 Solving 11.5 + x = 11.011357773 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 = 11.011357773 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.011357773 + -11.5 x = 11.011357773 + -11.5 Combine like terms: 11.011357773 + -11.5 = -0.488642227 x = -0.488642227 Simplifying x = -0.488642227Subproblem 2
x + 11.5 = -11.011357773 Simplifying x + 11.5 = -11.011357773 Reorder the terms: 11.5 + x = -11.011357773 Solving 11.5 + x = -11.011357773 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 = -11.011357773 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.011357773 + -11.5 x = -11.011357773 + -11.5 Combine like terms: -11.011357773 + -11.5 = -22.511357773 x = -22.511357773 Simplifying x = -22.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.488642227, -22.511357773}
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