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Simplifying x2 + 23x + -39 = 0 Reorder the terms: -39 + 23x + x2 = 0 Solving -39 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 23x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 23x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 23x + x2 = 0 + 39 23x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 23x + x2 = 39 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 = 39 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 39 + 132.25 Combine like terms: 39 + 132.25 = 171.25 132.25 + 23x + x2 = 171.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 171.25 Calculate the square root of the right side: 13.086252328 Break this problem into two subproblems by setting (x + 11.5) equal to 13.086252328 and -13.086252328.Subproblem 1
x + 11.5 = 13.086252328 Simplifying x + 11.5 = 13.086252328 Reorder the terms: 11.5 + x = 13.086252328 Solving 11.5 + x = 13.086252328 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 = 13.086252328 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 13.086252328 + -11.5 x = 13.086252328 + -11.5 Combine like terms: 13.086252328 + -11.5 = 1.586252328 x = 1.586252328 Simplifying x = 1.586252328Subproblem 2
x + 11.5 = -13.086252328 Simplifying x + 11.5 = -13.086252328 Reorder the terms: 11.5 + x = -13.086252328 Solving 11.5 + x = -13.086252328 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 = -13.086252328 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -13.086252328 + -11.5 x = -13.086252328 + -11.5 Combine like terms: -13.086252328 + -11.5 = -24.586252328 x = -24.586252328 Simplifying x = -24.586252328Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.586252328, -24.586252328}
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