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Simplifying x(x + 13) = x + 10(x + 1) Reorder the terms: x(13 + x) = x + 10(x + 1) (13 * x + x * x) = x + 10(x + 1) (13x + x2) = x + 10(x + 1) Reorder the terms: 13x + x2 = x + 10(1 + x) 13x + x2 = x + (1 * 10 + x * 10) 13x + x2 = x + (10 + 10x) Reorder the terms: 13x + x2 = 10 + x + 10x Combine like terms: x + 10x = 11x 13x + x2 = 10 + 11x Solving 13x + x2 = 10 + 11x Solving for variable 'x'. Reorder the terms: -10 + 13x + -11x + x2 = 10 + 11x + -10 + -11x Combine like terms: 13x + -11x = 2x -10 + 2x + x2 = 10 + 11x + -10 + -11x Reorder the terms: -10 + 2x + x2 = 10 + -10 + 11x + -11x Combine like terms: 10 + -10 = 0 -10 + 2x + x2 = 0 + 11x + -11x -10 + 2x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -10 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2x + x2 = 0 + 10 2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2x + x2 = 10 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + 2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2x + x2 = 11 Factor a perfect square on the left side: (x + 1)(x + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 1 = 3.31662479 Simplifying x + 1 = 3.31662479 Reorder the terms: 1 + x = 3.31662479 Solving 1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.31662479 + -1 x = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 x = 2.31662479 Simplifying x = 2.31662479Subproblem 2
x + 1 = -3.31662479 Simplifying x + 1 = -3.31662479 Reorder the terms: 1 + x = -3.31662479 Solving 1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.31662479 + -1 x = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 x = -4.31662479 Simplifying x = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31662479, -4.31662479}
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