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Simplifying x(x + 13) = x + 1(x + 10) Reorder the terms: x(13 + x) = x + 1(x + 10) (13 * x + x * x) = x + 1(x + 10) (13x + x2) = x + 1(x + 10) Reorder the terms: 13x + x2 = x + 1(10 + x) 13x + x2 = x + (10 * 1 + x * 1) 13x + x2 = x + (10 + 1x) Reorder the terms: 13x + x2 = 10 + x + 1x Combine like terms: x + 1x = 2x 13x + x2 = 10 + 2x Solving 13x + x2 = 10 + 2x Solving for variable 'x'. Reorder the terms: -10 + 13x + -2x + x2 = 10 + 2x + -10 + -2x Combine like terms: 13x + -2x = 11x -10 + 11x + x2 = 10 + 2x + -10 + -2x Reorder the terms: -10 + 11x + x2 = 10 + -10 + 2x + -2x Combine like terms: 10 + -10 = 0 -10 + 11x + x2 = 0 + 2x + -2x -10 + 11x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -10 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 11x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 11x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 11x + x2 = 0 + 10 11x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 11x + x2 = 10 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 = 10 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + 11x + x2 = 40.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 5.5 = 6.34428877 Simplifying x + 5.5 = 6.34428877 Reorder the terms: 5.5 + x = 6.34428877 Solving 5.5 + x = 6.34428877 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 = 6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.34428877 + -5.5 x = 6.34428877 + -5.5 Combine like terms: 6.34428877 + -5.5 = 0.84428877 x = 0.84428877 Simplifying x = 0.84428877Subproblem 2
x + 5.5 = -6.34428877 Simplifying x + 5.5 = -6.34428877 Reorder the terms: 5.5 + x = -6.34428877 Solving 5.5 + x = -6.34428877 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 = -6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.34428877 + -5.5 x = -6.34428877 + -5.5 Combine like terms: -6.34428877 + -5.5 = -11.84428877 x = -11.84428877 Simplifying x = -11.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.84428877, -11.84428877}
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