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Simplifying x2 + 23x + -600 = 0 Reorder the terms: -600 + 23x + x2 = 0 Solving -600 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + 23x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 23x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 23x + x2 = 0 + 600 23x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 23x + x2 = 600 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 = 600 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 600 + 132.25 Combine like terms: 600 + 132.25 = 732.25 132.25 + 23x + x2 = 732.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 732.25 Calculate the square root of the right side: 27.060118255 Break this problem into two subproblems by setting (x + 11.5) equal to 27.060118255 and -27.060118255.Subproblem 1
x + 11.5 = 27.060118255 Simplifying x + 11.5 = 27.060118255 Reorder the terms: 11.5 + x = 27.060118255 Solving 11.5 + x = 27.060118255 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 = 27.060118255 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 27.060118255 + -11.5 x = 27.060118255 + -11.5 Combine like terms: 27.060118255 + -11.5 = 15.560118255 x = 15.560118255 Simplifying x = 15.560118255Subproblem 2
x + 11.5 = -27.060118255 Simplifying x + 11.5 = -27.060118255 Reorder the terms: 11.5 + x = -27.060118255 Solving 11.5 + x = -27.060118255 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 = -27.060118255 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -27.060118255 + -11.5 x = -27.060118255 + -11.5 Combine like terms: -27.060118255 + -11.5 = -38.560118255 x = -38.560118255 Simplifying x = -38.560118255Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.560118255, -38.560118255}
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