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Simplifying x2 + -11 + 6x + 1 + 5x + 1 = 180 Reorder the terms: -11 + 1 + 1 + 6x + 5x + x2 = 180 Combine like terms: -11 + 1 = -10 -10 + 1 + 6x + 5x + x2 = 180 Combine like terms: -10 + 1 = -9 -9 + 6x + 5x + x2 = 180 Combine like terms: 6x + 5x = 11x -9 + 11x + x2 = 180 Solving -9 + 11x + x2 = 180 Solving for variable 'x'. Reorder the terms: -9 + -180 + 11x + x2 = 180 + -180 Combine like terms: -9 + -180 = -189 -189 + 11x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -189 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '189' to each side of the equation. -189 + 11x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + 11x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + 11x + x2 = 0 + 189 11x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 11x + x2 = 189 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 = 189 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 189 + 30.25 Combine like terms: 189 + 30.25 = 219.25 30.25 + 11x + x2 = 219.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 219.25 Calculate the square root of the right side: 14.807092895 Break this problem into two subproblems by setting (x + 5.5) equal to 14.807092895 and -14.807092895.Subproblem 1
x + 5.5 = 14.807092895 Simplifying x + 5.5 = 14.807092895 Reorder the terms: 5.5 + x = 14.807092895 Solving 5.5 + x = 14.807092895 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 = 14.807092895 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 14.807092895 + -5.5 x = 14.807092895 + -5.5 Combine like terms: 14.807092895 + -5.5 = 9.307092895 x = 9.307092895 Simplifying x = 9.307092895Subproblem 2
x + 5.5 = -14.807092895 Simplifying x + 5.5 = -14.807092895 Reorder the terms: 5.5 + x = -14.807092895 Solving 5.5 + x = -14.807092895 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 = -14.807092895 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -14.807092895 + -5.5 x = -14.807092895 + -5.5 Combine like terms: -14.807092895 + -5.5 = -20.307092895 x = -20.307092895 Simplifying x = -20.307092895Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.307092895, -20.307092895}
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