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Simplifying X(X + 11) = 198 Reorder the terms: X(11 + X) = 198 (11 * X + X * X) = 198 (11X + X2) = 198 Solving 11X + X2 = 198 Solving for variable 'X'. Reorder the terms: -198 + 11X + X2 = 198 + -198 Combine like terms: 198 + -198 = 0 -198 + 11X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 11X + 198 + X2 = 0 + 198 Reorder the terms: -198 + 198 + 11X + X2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 11X + X2 = 0 + 198 11X + X2 = 0 + 198 Combine like terms: 0 + 198 = 198 11X + X2 = 198 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 = 198 + 30.25 Reorder the terms: 30.25 + 11X + X2 = 198 + 30.25 Combine like terms: 198 + 30.25 = 228.25 30.25 + 11X + X2 = 228.25 Factor a perfect square on the left side: (X + 5.5)(X + 5.5) = 228.25 Calculate the square root of the right side: 15.10794493 Break this problem into two subproblems by setting (X + 5.5) equal to 15.10794493 and -15.10794493.Subproblem 1
X + 5.5 = 15.10794493 Simplifying X + 5.5 = 15.10794493 Reorder the terms: 5.5 + X = 15.10794493 Solving 5.5 + X = 15.10794493 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 = 15.10794493 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + X = 15.10794493 + -5.5 X = 15.10794493 + -5.5 Combine like terms: 15.10794493 + -5.5 = 9.60794493 X = 9.60794493 Simplifying X = 9.60794493Subproblem 2
X + 5.5 = -15.10794493 Simplifying X + 5.5 = -15.10794493 Reorder the terms: 5.5 + X = -15.10794493 Solving 5.5 + X = -15.10794493 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 = -15.10794493 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + X = -15.10794493 + -5.5 X = -15.10794493 + -5.5 Combine like terms: -15.10794493 + -5.5 = -20.60794493 X = -20.60794493 Simplifying X = -20.60794493Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.60794493, -20.60794493}
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