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Simplifying X2 + -11X + -18 = 0 Reorder the terms: -18 + -11X + X2 = 0 Solving -18 + -11X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -11X + 18 + X2 = 0 + 18 Reorder the terms: -18 + 18 + -11X + X2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -11X + X2 = 0 + 18 -11X + X2 = 0 + 18 Combine like terms: 0 + 18 = 18 -11X + X2 = 18 The X term is -11X. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11X + 30.25 + X2 = 18 + 30.25 Reorder the terms: 30.25 + -11X + X2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + -11X + X2 = 48.25 Factor a perfect square on the left side: (X + -5.5)(X + -5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (X + -5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
X + -5.5 = 6.946221995 Simplifying X + -5.5 = 6.946221995 Reorder the terms: -5.5 + X = 6.946221995 Solving -5.5 + X = 6.946221995 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 6.946221995 + 5.5 X = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 X = 12.446221995 Simplifying X = 12.446221995Subproblem 2
X + -5.5 = -6.946221995 Simplifying X + -5.5 = -6.946221995 Reorder the terms: -5.5 + X = -6.946221995 Solving -5.5 + X = -6.946221995 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -6.946221995 + 5.5 X = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 X = -1.446221995 Simplifying X = -1.446221995Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.446221995, -1.446221995}
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