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Simplifying x2 + -19x + 23 = 0 Reorder the terms: 23 + -19x + x2 = 0 Solving 23 + -19x + 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 + -19x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -19x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -19x + x2 = 0 + -23 -19x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -19x + x2 = -23 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -23 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -23 + 90.25 Combine like terms: -23 + 90.25 = 67.25 90.25 + -19x + x2 = 67.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + -9.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + -9.5 = 8.200609733 Simplifying x + -9.5 = 8.200609733 Reorder the terms: -9.5 + x = 8.200609733 Solving -9.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.200609733 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.200609733 + 9.5 x = 8.200609733 + 9.5 Combine like terms: 8.200609733 + 9.5 = 17.700609733 x = 17.700609733 Simplifying x = 17.700609733Subproblem 2
x + -9.5 = -8.200609733 Simplifying x + -9.5 = -8.200609733 Reorder the terms: -9.5 + x = -8.200609733 Solving -9.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.200609733 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.200609733 + 9.5 x = -8.200609733 + 9.5 Combine like terms: -8.200609733 + 9.5 = 1.299390267 x = 1.299390267 Simplifying x = 1.299390267Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.700609733, 1.299390267}
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