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Simplifying x2 + -10x + 23 = 0 Reorder the terms: 23 + -10x + x2 = 0 Solving 23 + -10x + 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 + -10x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -10x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -10x + x2 = 0 + -23 -10x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -10x + x2 = -23 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -23 + 25 Reorder the terms: 25 + -10x + x2 = -23 + 25 Combine like terms: -23 + 25 = 2 25 + -10x + x2 = 2 Factor a perfect square on the left side: (x + -5)(x + -5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -5 = 1.414213562 Simplifying x + -5 = 1.414213562 Reorder the terms: -5 + x = 1.414213562 Solving -5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.414213562 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.414213562 + 5 x = 1.414213562 + 5 Combine like terms: 1.414213562 + 5 = 6.414213562 x = 6.414213562 Simplifying x = 6.414213562Subproblem 2
x + -5 = -1.414213562 Simplifying x + -5 = -1.414213562 Reorder the terms: -5 + x = -1.414213562 Solving -5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.414213562 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.414213562 + 5 x = -1.414213562 + 5 Combine like terms: -1.414213562 + 5 = 3.585786438 x = 3.585786438 Simplifying x = 3.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.414213562, 3.585786438}
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