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Simplifying x(x + 1) + (x + 2) = 24 Reorder the terms: x(1 + x) + (x + 2) = 24 (1 * x + x * x) + (x + 2) = 24 (1x + x2) + (x + 2) = 24 Reorder the terms: 1x + x2 + (2 + x) = 24 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 24 Reorder the terms: 2 + 1x + x + x2 = 24 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 24 Solving 2 + 2x + x2 = 24 Solving for variable 'x'. Reorder the terms: 2 + -24 + 2x + x2 = 24 + -24 Combine like terms: 2 + -24 = -22 -22 + 2x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -22 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 2x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 2x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2x + x2 = 0 + 22 2x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 2x + x2 = 22 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 = 22 + 1 Reorder the terms: 1 + 2x + x2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + 2x + x2 = 23 Factor a perfect square on the left side: (x + 1)(x + 1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 1) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 1 = 4.795831523 Simplifying x + 1 = 4.795831523 Reorder the terms: 1 + x = 4.795831523 Solving 1 + x = 4.795831523 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 = 4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.795831523 + -1 x = 4.795831523 + -1 Combine like terms: 4.795831523 + -1 = 3.795831523 x = 3.795831523 Simplifying x = 3.795831523Subproblem 2
x + 1 = -4.795831523 Simplifying x + 1 = -4.795831523 Reorder the terms: 1 + x = -4.795831523 Solving 1 + x = -4.795831523 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 = -4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.795831523 + -1 x = -4.795831523 + -1 Combine like terms: -4.795831523 + -1 = -5.795831523 x = -5.795831523 Simplifying x = -5.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.795831523, -5.795831523}
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