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Simplifying (x + 1)(x + 10) = 22 + 1 Reorder the terms: (1 + x)(x + 10) = 22 + 1 Reorder the terms: (1 + x)(10 + x) = 22 + 1 Multiply (1 + x) * (10 + x) (1(10 + x) + x(10 + x)) = 22 + 1 ((10 * 1 + x * 1) + x(10 + x)) = 22 + 1 ((10 + 1x) + x(10 + x)) = 22 + 1 (10 + 1x + (10 * x + x * x)) = 22 + 1 (10 + 1x + (10x + x2)) = 22 + 1 Combine like terms: 1x + 10x = 11x (10 + 11x + x2) = 22 + 1 Combine like terms: 22 + 1 = 23 10 + 11x + x2 = 23 Solving 10 + 11x + x2 = 23 Solving for variable 'x'. Reorder the terms: 10 + -23 + 11x + x2 = 23 + -23 Combine like terms: 10 + -23 = -13 -13 + 11x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -13 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 11x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 11x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 11x + x2 = 0 + 13 11x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 11x + x2 = 13 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 = 13 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 13 + 30.25 Combine like terms: 13 + 30.25 = 43.25 30.25 + 11x + x2 = 43.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 5.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + 5.5 = 6.576473219 Simplifying x + 5.5 = 6.576473219 Reorder the terms: 5.5 + x = 6.576473219 Solving 5.5 + x = 6.576473219 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 = 6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.576473219 + -5.5 x = 6.576473219 + -5.5 Combine like terms: 6.576473219 + -5.5 = 1.076473219 x = 1.076473219 Simplifying x = 1.076473219Subproblem 2
x + 5.5 = -6.576473219 Simplifying x + 5.5 = -6.576473219 Reorder the terms: 5.5 + x = -6.576473219 Solving 5.5 + x = -6.576473219 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 = -6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.576473219 + -5.5 x = -6.576473219 + -5.5 Combine like terms: -6.576473219 + -5.5 = -12.076473219 x = -12.076473219 Simplifying x = -12.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.076473219, -12.076473219}
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