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Simplifying x2 + -1x + -612 = 0 Reorder the terms: -612 + -1x + x2 = 0 Solving -612 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '612' to each side of the equation. -612 + -1x + 612 + x2 = 0 + 612 Reorder the terms: -612 + 612 + -1x + x2 = 0 + 612 Combine like terms: -612 + 612 = 0 0 + -1x + x2 = 0 + 612 -1x + x2 = 0 + 612 Combine like terms: 0 + 612 = 612 -1x + x2 = 612 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 612 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 612 + 0.25 Combine like terms: 612 + 0.25 = 612.25 0.25 + -1x + x2 = 612.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 612.25 Calculate the square root of the right side: 24.743686063 Break this problem into two subproblems by setting (x + -0.5) equal to 24.743686063 and -24.743686063.Subproblem 1
x + -0.5 = 24.743686063 Simplifying x + -0.5 = 24.743686063 Reorder the terms: -0.5 + x = 24.743686063 Solving -0.5 + x = 24.743686063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 24.743686063 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 24.743686063 + 0.5 x = 24.743686063 + 0.5 Combine like terms: 24.743686063 + 0.5 = 25.243686063 x = 25.243686063 Simplifying x = 25.243686063Subproblem 2
x + -0.5 = -24.743686063 Simplifying x + -0.5 = -24.743686063 Reorder the terms: -0.5 + x = -24.743686063 Solving -0.5 + x = -24.743686063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -24.743686063 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -24.743686063 + 0.5 x = -24.743686063 + 0.5 Combine like terms: -24.743686063 + 0.5 = -24.243686063 x = -24.243686063 Simplifying x = -24.243686063Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.243686063, -24.243686063}
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