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Simplifying x2 + 23x + -4 = 0 Reorder the terms: -4 + 23x + x2 = 0 Solving -4 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 23x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 23x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 23x + x2 = 0 + 4 23x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 23x + x2 = 4 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 = 4 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 4 + 132.25 Combine like terms: 4 + 132.25 = 136.25 132.25 + 23x + x2 = 136.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + 11.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + 11.5 = 11.67261753 Simplifying x + 11.5 = 11.67261753 Reorder the terms: 11.5 + x = 11.67261753 Solving 11.5 + x = 11.67261753 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 = 11.67261753 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 11.67261753 + -11.5 x = 11.67261753 + -11.5 Combine like terms: 11.67261753 + -11.5 = 0.17261753 x = 0.17261753 Simplifying x = 0.17261753Subproblem 2
x + 11.5 = -11.67261753 Simplifying x + 11.5 = -11.67261753 Reorder the terms: 11.5 + x = -11.67261753 Solving 11.5 + x = -11.67261753 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 = -11.67261753 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -11.67261753 + -11.5 x = -11.67261753 + -11.5 Combine like terms: -11.67261753 + -11.5 = -23.17261753 x = -23.17261753 Simplifying x = -23.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17261753, -23.17261753}
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