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Simplifying X2 + -5X + -23 = 0 Reorder the terms: -23 + -5X + X2 = 0 Solving -23 + -5X + 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 + -5X + 23 + X2 = 0 + 23 Reorder the terms: -23 + 23 + -5X + X2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -5X + X2 = 0 + 23 -5X + X2 = 0 + 23 Combine like terms: 0 + 23 = 23 -5X + X2 = 23 The X term is -5X. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5X + 6.25 + X2 = 23 + 6.25 Reorder the terms: 6.25 + -5X + X2 = 23 + 6.25 Combine like terms: 23 + 6.25 = 29.25 6.25 + -5X + X2 = 29.25 Factor a perfect square on the left side: (X + -2.5)(X + -2.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (X + -2.5) equal to 5.408326913 and -5.408326913.Subproblem 1
X + -2.5 = 5.408326913 Simplifying X + -2.5 = 5.408326913 Reorder the terms: -2.5 + X = 5.408326913 Solving -2.5 + X = 5.408326913 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = 5.408326913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = 5.408326913 + 2.5 X = 5.408326913 + 2.5 Combine like terms: 5.408326913 + 2.5 = 7.908326913 X = 7.908326913 Simplifying X = 7.908326913Subproblem 2
X + -2.5 = -5.408326913 Simplifying X + -2.5 = -5.408326913 Reorder the terms: -2.5 + X = -5.408326913 Solving -2.5 + X = -5.408326913 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = -5.408326913 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = -5.408326913 + 2.5 X = -5.408326913 + 2.5 Combine like terms: -5.408326913 + 2.5 = -2.908326913 X = -2.908326913 Simplifying X = -2.908326913Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.908326913, -2.908326913}
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