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Simplifying x2 + 11x = 196 Reorder the terms: 11x + x2 = 196 Solving 11x + x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 11x + x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 11x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 11x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 11x + x2 = 0 + 196 11x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 11x + x2 = 196 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 = 196 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 196 + 30.25 Combine like terms: 196 + 30.25 = 226.25 30.25 + 11x + x2 = 226.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 226.25 Calculate the square root of the right side: 15.041608956 Break this problem into two subproblems by setting (x + 5.5) equal to 15.041608956 and -15.041608956.Subproblem 1
x + 5.5 = 15.041608956 Simplifying x + 5.5 = 15.041608956 Reorder the terms: 5.5 + x = 15.041608956 Solving 5.5 + x = 15.041608956 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 = 15.041608956 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 15.041608956 + -5.5 x = 15.041608956 + -5.5 Combine like terms: 15.041608956 + -5.5 = 9.541608956 x = 9.541608956 Simplifying x = 9.541608956Subproblem 2
x + 5.5 = -15.041608956 Simplifying x + 5.5 = -15.041608956 Reorder the terms: 5.5 + x = -15.041608956 Solving 5.5 + x = -15.041608956 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 = -15.041608956 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -15.041608956 + -5.5 x = -15.041608956 + -5.5 Combine like terms: -15.041608956 + -5.5 = -20.541608956 x = -20.541608956 Simplifying x = -20.541608956Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.541608956, -20.541608956}
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