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Simplifying x2 + -23x + -23 = 0 Reorder the terms: -23 + -23x + x2 = 0 Solving -23 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -23x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -23x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -23x + x2 = 0 + 23 -23x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -23x + x2 = 23 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 = 23 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 23 + 132.25 Combine like terms: 23 + 132.25 = 155.25 132.25 + -23x + x2 = 155.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (x + -11.5) equal to 12.459935794 and -12.459935794.Subproblem 1
x + -11.5 = 12.459935794 Simplifying x + -11.5 = 12.459935794 Reorder the terms: -11.5 + x = 12.459935794 Solving -11.5 + x = 12.459935794 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 = 12.459935794 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 12.459935794 + 11.5 x = 12.459935794 + 11.5 Combine like terms: 12.459935794 + 11.5 = 23.959935794 x = 23.959935794 Simplifying x = 23.959935794Subproblem 2
x + -11.5 = -12.459935794 Simplifying x + -11.5 = -12.459935794 Reorder the terms: -11.5 + x = -12.459935794 Solving -11.5 + x = -12.459935794 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 = -12.459935794 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -12.459935794 + 11.5 x = -12.459935794 + 11.5 Combine like terms: -12.459935794 + 11.5 = -0.959935794 x = -0.959935794 Simplifying x = -0.959935794Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.959935794, -0.959935794}
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