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Simplifying (x + 11)(x + 11) = 13 Reorder the terms: (11 + x)(x + 11) = 13 Reorder the terms: (11 + x)(11 + x) = 13 Multiply (11 + x) * (11 + x) (11(11 + x) + x(11 + x)) = 13 ((11 * 11 + x * 11) + x(11 + x)) = 13 ((121 + 11x) + x(11 + x)) = 13 (121 + 11x + (11 * x + x * x)) = 13 (121 + 11x + (11x + x2)) = 13 Combine like terms: 11x + 11x = 22x (121 + 22x + x2) = 13 Solving 121 + 22x + x2 = 13 Solving for variable 'x'. Reorder the terms: 121 + -13 + 22x + x2 = 13 + -13 Combine like terms: 121 + -13 = 108 108 + 22x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 108 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + 22x + -108 + x2 = 0 + -108 Reorder the terms: 108 + -108 + 22x + x2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + 22x + x2 = 0 + -108 22x + x2 = 0 + -108 Combine like terms: 0 + -108 = -108 22x + x2 = -108 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 = -108 + 121 Reorder the terms: 121 + 22x + x2 = -108 + 121 Combine like terms: -108 + 121 = 13 121 + 22x + x2 = 13 Factor a perfect square on the left side: (x + 11)(x + 11) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 11) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 11 = 3.605551275 Simplifying x + 11 = 3.605551275 Reorder the terms: 11 + x = 3.605551275 Solving 11 + x = 3.605551275 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 = 3.605551275 + -11 Combine like terms: 11 + -11 = 0 0 + x = 3.605551275 + -11 x = 3.605551275 + -11 Combine like terms: 3.605551275 + -11 = -7.394448725 x = -7.394448725 Simplifying x = -7.394448725Subproblem 2
x + 11 = -3.605551275 Simplifying x + 11 = -3.605551275 Reorder the terms: 11 + x = -3.605551275 Solving 11 + x = -3.605551275 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 = -3.605551275 + -11 Combine like terms: 11 + -11 = 0 0 + x = -3.605551275 + -11 x = -3.605551275 + -11 Combine like terms: -3.605551275 + -11 = -14.605551275 x = -14.605551275 Simplifying x = -14.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.394448725, -14.605551275}
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