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Simplifying X2 + X + -612 = 0 Reorder the terms: -612 + X + X2 = 0 Solving -612 + X + 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 + X + 612 + X2 = 0 + 612 Reorder the terms: -612 + 612 + X + X2 = 0 + 612 Combine like terms: -612 + 612 = 0 0 + X + X2 = 0 + 612 X + X2 = 0 + 612 Combine like terms: 0 + 612 = 612 X + X2 = 612 The X term is X. 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. X + 0.25 + X2 = 612 + 0.25 Reorder the terms: 0.25 + X + X2 = 612 + 0.25 Combine like terms: 612 + 0.25 = 612.25 0.25 + X + 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 = 24.243686063 X = 24.243686063 Simplifying X = 24.243686063Subproblem 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 = -25.243686063 X = -25.243686063 Simplifying X = -25.243686063Solution
The solution to the problem is based on the solutions from the subproblems. X = {24.243686063, -25.243686063}
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