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Simplifying x(x + 1) + (x + 2) + (x + 3) + (x + 4) = 28 Reorder the terms: x(1 + x) + (x + 2) + (x + 3) + (x + 4) = 28 (1 * x + x * x) + (x + 2) + (x + 3) + (x + 4) = 28 (1x + x2) + (x + 2) + (x + 3) + (x + 4) = 28 Reorder the terms: 1x + x2 + (2 + x) + (x + 3) + (x + 4) = 28 Remove parenthesis around (2 + x) 1x + x2 + 2 + x + (x + 3) + (x + 4) = 28 Reorder the terms: 1x + x2 + 2 + x + (3 + x) + (x + 4) = 28 Remove parenthesis around (3 + x) 1x + x2 + 2 + x + 3 + x + (x + 4) = 28 Reorder the terms: 1x + x2 + 2 + x + 3 + x + (4 + x) = 28 Remove parenthesis around (4 + x) 1x + x2 + 2 + x + 3 + x + 4 + x = 28 Reorder the terms: 2 + 3 + 4 + 1x + x + x + x + x2 = 28 Combine like terms: 2 + 3 = 5 5 + 4 + 1x + x + x + x + x2 = 28 Combine like terms: 5 + 4 = 9 9 + 1x + x + x + x + x2 = 28 Combine like terms: 1x + x = 2x 9 + 2x + x + x + x2 = 28 Combine like terms: 2x + x = 3x 9 + 3x + x + x2 = 28 Combine like terms: 3x + x = 4x 9 + 4x + x2 = 28 Solving 9 + 4x + x2 = 28 Solving for variable 'x'. Reorder the terms: 9 + -28 + 4x + x2 = 28 + -28 Combine like terms: 9 + -28 = -19 -19 + 4x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -19 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 4x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 4x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 4x + x2 = 0 + 19 4x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 4x + x2 = 19 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 19 + 4 Reorder the terms: 4 + 4x + x2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + 4x + x2 = 23 Factor a perfect square on the left side: (x + 2)(x + 2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 2) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 2 = 4.795831523 Simplifying x + 2 = 4.795831523 Reorder the terms: 2 + x = 4.795831523 Solving 2 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.795831523 + -2 x = 4.795831523 + -2 Combine like terms: 4.795831523 + -2 = 2.795831523 x = 2.795831523 Simplifying x = 2.795831523Subproblem 2
x + 2 = -4.795831523 Simplifying x + 2 = -4.795831523 Reorder the terms: 2 + x = -4.795831523 Solving 2 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.795831523 + -2 x = -4.795831523 + -2 Combine like terms: -4.795831523 + -2 = -6.795831523 x = -6.795831523 Simplifying x = -6.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.795831523, -6.795831523}
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