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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 = 130 121 + 22x + x2 = 130 Factor a perfect square on the left side: (x + 11)(x + 11) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 11) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 11 = 11.401754251 Simplifying x + 11 = 11.401754251 Reorder the terms: 11 + x = 11.401754251 Solving 11 + x = 11.401754251 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 = 11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.401754251 + -11 x = 11.401754251 + -11 Combine like terms: 11.401754251 + -11 = 0.401754251 x = 0.401754251 Simplifying x = 0.401754251Subproblem 2
x + 11 = -11.401754251 Simplifying x + 11 = -11.401754251 Reorder the terms: 11 + x = -11.401754251 Solving 11 + x = -11.401754251 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 = -11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.401754251 + -11 x = -11.401754251 + -11 Combine like terms: -11.401754251 + -11 = -22.401754251 x = -22.401754251 Simplifying x = -22.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.401754251, -22.401754251}
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