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Simplifying x2 + -23x + 92 = 0 Reorder the terms: 92 + -23x + x2 = 0 Solving 92 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-92' to each side of the equation. 92 + -23x + -92 + x2 = 0 + -92 Reorder the terms: 92 + -92 + -23x + x2 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -23x + x2 = 0 + -92 -23x + x2 = 0 + -92 Combine like terms: 0 + -92 = -92 -23x + x2 = -92 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 = -92 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -92 + 132.25 Combine like terms: -92 + 132.25 = 40.25 132.25 + -23x + x2 = 40.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -11.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -11.5 = 6.34428877 Simplifying x + -11.5 = 6.34428877 Reorder the terms: -11.5 + x = 6.34428877 Solving -11.5 + x = 6.34428877 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 = 6.34428877 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 6.34428877 + 11.5 x = 6.34428877 + 11.5 Combine like terms: 6.34428877 + 11.5 = 17.84428877 x = 17.84428877 Simplifying x = 17.84428877Subproblem 2
x + -11.5 = -6.34428877 Simplifying x + -11.5 = -6.34428877 Reorder the terms: -11.5 + x = -6.34428877 Solving -11.5 + x = -6.34428877 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 = -6.34428877 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -6.34428877 + 11.5 x = -6.34428877 + 11.5 Combine like terms: -6.34428877 + 11.5 = 5.15571123 x = 5.15571123 Simplifying x = 5.15571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.84428877, 5.15571123}
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