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Simplifying x2 + 11x + -182 = 0 Reorder the terms: -182 + 11x + x2 = 0 Solving -182 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '182' to each side of the equation. -182 + 11x + 182 + x2 = 0 + 182 Reorder the terms: -182 + 182 + 11x + x2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 11x + x2 = 0 + 182 11x + x2 = 0 + 182 Combine like terms: 0 + 182 = 182 11x + x2 = 182 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 = 182 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 182 + 30.25 Combine like terms: 182 + 30.25 = 212.25 30.25 + 11x + x2 = 212.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 212.25 Calculate the square root of the right side: 14.568802284 Break this problem into two subproblems by setting (x + 5.5) equal to 14.568802284 and -14.568802284.Subproblem 1
x + 5.5 = 14.568802284 Simplifying x + 5.5 = 14.568802284 Reorder the terms: 5.5 + x = 14.568802284 Solving 5.5 + x = 14.568802284 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 = 14.568802284 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 14.568802284 + -5.5 x = 14.568802284 + -5.5 Combine like terms: 14.568802284 + -5.5 = 9.068802284 x = 9.068802284 Simplifying x = 9.068802284Subproblem 2
x + 5.5 = -14.568802284 Simplifying x + 5.5 = -14.568802284 Reorder the terms: 5.5 + x = -14.568802284 Solving 5.5 + x = -14.568802284 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 = -14.568802284 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -14.568802284 + -5.5 x = -14.568802284 + -5.5 Combine like terms: -14.568802284 + -5.5 = -20.068802284 x = -20.068802284 Simplifying x = -20.068802284Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.068802284, -20.068802284}
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