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Simplifying (x + 3)(x + 2) = 39 Reorder the terms: (3 + x)(x + 2) = 39 Reorder the terms: (3 + x)(2 + x) = 39 Multiply (3 + x) * (2 + x) (3(2 + x) + x(2 + x)) = 39 ((2 * 3 + x * 3) + x(2 + x)) = 39 ((6 + 3x) + x(2 + x)) = 39 (6 + 3x + (2 * x + x * x)) = 39 (6 + 3x + (2x + x2)) = 39 Combine like terms: 3x + 2x = 5x (6 + 5x + x2) = 39 Solving 6 + 5x + x2 = 39 Solving for variable 'x'. Reorder the terms: 6 + -39 + 5x + x2 = 39 + -39 Combine like terms: 6 + -39 = -33 -33 + 5x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -33 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 5x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 5x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 5x + x2 = 0 + 33 5x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 5x + x2 = 33 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 33 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 33 + 6.25 Combine like terms: 33 + 6.25 = 39.25 6.25 + 5x + x2 = 39.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 2.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 2.5 = 6.264982043 Simplifying x + 2.5 = 6.264982043 Reorder the terms: 2.5 + x = 6.264982043 Solving 2.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.264982043 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.264982043 + -2.5 x = 6.264982043 + -2.5 Combine like terms: 6.264982043 + -2.5 = 3.764982043 x = 3.764982043 Simplifying x = 3.764982043Subproblem 2
x + 2.5 = -6.264982043 Simplifying x + 2.5 = -6.264982043 Reorder the terms: 2.5 + x = -6.264982043 Solving 2.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.264982043 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.264982043 + -2.5 x = -6.264982043 + -2.5 Combine like terms: -6.264982043 + -2.5 = -8.764982043 x = -8.764982043 Simplifying x = -8.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.764982043, -8.764982043}
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