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Simplifying (1x + 11)(1x + 11) = 104 Reorder the terms: (11 + 1x)(1x + 11) = 104 Reorder the terms: (11 + 1x)(11 + 1x) = 104 Multiply (11 + 1x) * (11 + 1x) (11(11 + 1x) + 1x * (11 + 1x)) = 104 ((11 * 11 + 1x * 11) + 1x * (11 + 1x)) = 104 ((121 + 11x) + 1x * (11 + 1x)) = 104 (121 + 11x + (11 * 1x + 1x * 1x)) = 104 (121 + 11x + (11x + 1x2)) = 104 Combine like terms: 11x + 11x = 22x (121 + 22x + 1x2) = 104 Solving 121 + 22x + 1x2 = 104 Solving for variable 'x'. Reorder the terms: 121 + -104 + 22x + 1x2 = 104 + -104 Combine like terms: 121 + -104 = 17 17 + 22x + 1x2 = 104 + -104 Combine like terms: 104 + -104 = 0 17 + 22x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 22x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 22x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 22x + x2 = 0 + -17 22x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 22x + x2 = -17 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 = -17 + 121 Reorder the terms: 121 + 22x + x2 = -17 + 121 Combine like terms: -17 + 121 = 104 121 + 22x + x2 = 104 Factor a perfect square on the left side: (x + 11)(x + 11) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 11) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 11 = 10.198039027 Simplifying x + 11 = 10.198039027 Reorder the terms: 11 + x = 10.198039027 Solving 11 + x = 10.198039027 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 = 10.198039027 + -11 Combine like terms: 11 + -11 = 0 0 + x = 10.198039027 + -11 x = 10.198039027 + -11 Combine like terms: 10.198039027 + -11 = -0.801960973 x = -0.801960973 Simplifying x = -0.801960973Subproblem 2
x + 11 = -10.198039027 Simplifying x + 11 = -10.198039027 Reorder the terms: 11 + x = -10.198039027 Solving 11 + x = -10.198039027 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 = -10.198039027 + -11 Combine like terms: 11 + -11 = 0 0 + x = -10.198039027 + -11 x = -10.198039027 + -11 Combine like terms: -10.198039027 + -11 = -21.198039027 x = -21.198039027 Simplifying x = -21.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.801960973, -21.198039027}
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