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Simplifying x2 + 22x = -9 Reorder the terms: 22x + x2 = -9 Solving 22x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 22x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 22x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 22x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 22x + x2 = 0 + -9 22x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 22x + x2 = -9 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -9 + 121 Reorder the terms: 121 + 22x + x2 = -9 + 121 Combine like terms: -9 + 121 = 112 121 + 22x + x2 = 112 Factor a perfect square on the left side: (x + 11)(x + 11) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + 11) equal to 10.583005244 and -10.583005244.Subproblem 1
x + 11 = 10.583005244 Simplifying x + 11 = 10.583005244 Reorder the terms: 11 + x = 10.583005244 Solving 11 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 10.583005244 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.583005244 + -11 x = 10.583005244 + -11 Combine like terms: 10.583005244 + -11 = -0.416994756 x = -0.416994756 Simplifying x = -0.416994756Subproblem 2
x + 11 = -10.583005244 Simplifying x + 11 = -10.583005244 Reorder the terms: 11 + x = -10.583005244 Solving 11 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -10.583005244 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.583005244 + -11 x = -10.583005244 + -11 Combine like terms: -10.583005244 + -11 = -21.583005244 x = -21.583005244 Simplifying x = -21.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.416994756, -21.583005244}
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