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Simplifying x2 + 11x = 23 Reorder the terms: 11x + x2 = 23 Solving 11x + x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + 11x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 11x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 11x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 11x + x2 = 0 + 23 11x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 11x + x2 = 23 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 = 23 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 23 + 30.25 Combine like terms: 23 + 30.25 = 53.25 30.25 + 11x + x2 = 53.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + 5.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + 5.5 = 7.29725976 Simplifying x + 5.5 = 7.29725976 Reorder the terms: 5.5 + x = 7.29725976 Solving 5.5 + x = 7.29725976 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 = 7.29725976 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.29725976 + -5.5 x = 7.29725976 + -5.5 Combine like terms: 7.29725976 + -5.5 = 1.79725976 x = 1.79725976 Simplifying x = 1.79725976Subproblem 2
x + 5.5 = -7.29725976 Simplifying x + 5.5 = -7.29725976 Reorder the terms: 5.5 + x = -7.29725976 Solving 5.5 + x = -7.29725976 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 = -7.29725976 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.29725976 + -5.5 x = -7.29725976 + -5.5 Combine like terms: -7.29725976 + -5.5 = -12.79725976 x = -12.79725976 Simplifying x = -12.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.79725976, -12.79725976}
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