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Simplifying 198 = (x + 11)(x) Reorder the terms: 198 = (11 + x)(x) Reorder the terms for easier multiplication: 198 = x(11 + x) 198 = (11 * x + x * x) 198 = (11x + x2) Solving 198 = 11x + x2 Solving for variable 'x'. Reorder the terms: 198 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 198 + -11x + -1x2 = 0 + x2 + -1x2 198 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 198 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -198 + 11x + x2 = 0 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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