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Simplifying (x2) + 11x + -147 = 0 x2 + 11x + -147 = 0 Reorder the terms: -147 + 11x + x2 = 0 Solving -147 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 11x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 11x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 11x + x2 = 0 + 147 11x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 11x + x2 = 147 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 = 147 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 147 + 30.25 Combine like terms: 147 + 30.25 = 177.25 30.25 + 11x + x2 = 177.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (x + 5.5) equal to 13.313526956 and -13.313526956.Subproblem 1
x + 5.5 = 13.313526956 Simplifying x + 5.5 = 13.313526956 Reorder the terms: 5.5 + x = 13.313526956 Solving 5.5 + x = 13.313526956 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 = 13.313526956 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 13.313526956 + -5.5 x = 13.313526956 + -5.5 Combine like terms: 13.313526956 + -5.5 = 7.813526956 x = 7.813526956 Simplifying x = 7.813526956Subproblem 2
x + 5.5 = -13.313526956 Simplifying x + 5.5 = -13.313526956 Reorder the terms: 5.5 + x = -13.313526956 Solving 5.5 + x = -13.313526956 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 = -13.313526956 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -13.313526956 + -5.5 x = -13.313526956 + -5.5 Combine like terms: -13.313526956 + -5.5 = -18.813526956 x = -18.813526956 Simplifying x = -18.813526956Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.813526956, -18.813526956}
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