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Simplifying x2 + -23x + 10 = 0 Reorder the terms: 10 + -23x + x2 = 0 Solving 10 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -23x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -23x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -23x + x2 = 0 + -10 -23x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -23x + x2 = -10 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 = -10 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -10 + 132.25 Combine like terms: -10 + 132.25 = 122.25 132.25 + -23x + x2 = 122.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + -11.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + -11.5 = 11.056672194 Simplifying x + -11.5 = 11.056672194 Reorder the terms: -11.5 + x = 11.056672194 Solving -11.5 + x = 11.056672194 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 = 11.056672194 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.056672194 + 11.5 x = 11.056672194 + 11.5 Combine like terms: 11.056672194 + 11.5 = 22.556672194 x = 22.556672194 Simplifying x = 22.556672194Subproblem 2
x + -11.5 = -11.056672194 Simplifying x + -11.5 = -11.056672194 Reorder the terms: -11.5 + x = -11.056672194 Solving -11.5 + x = -11.056672194 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 = -11.056672194 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.056672194 + 11.5 x = -11.056672194 + 11.5 Combine like terms: -11.056672194 + 11.5 = 0.443327806 x = 0.443327806 Simplifying x = 0.443327806Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.556672194, 0.443327806}
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