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Simplifying (x + 6)(x + -3) = 8 Reorder the terms: (6 + x)(x + -3) = 8 Reorder the terms: (6 + x)(-3 + x) = 8 Multiply (6 + x) * (-3 + x) (6(-3 + x) + x(-3 + x)) = 8 ((-3 * 6 + x * 6) + x(-3 + x)) = 8 ((-18 + 6x) + x(-3 + x)) = 8 (-18 + 6x + (-3 * x + x * x)) = 8 (-18 + 6x + (-3x + x2)) = 8 Combine like terms: 6x + -3x = 3x (-18 + 3x + x2) = 8 Solving -18 + 3x + x2 = 8 Solving for variable 'x'. Reorder the terms: -18 + -8 + 3x + x2 = 8 + -8 Combine like terms: -18 + -8 = -26 -26 + 3x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -26 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 3x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 3x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 3x + x2 = 0 + 26 3x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 3x + x2 = 26 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 26 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 26 + 2.25 Combine like terms: 26 + 2.25 = 28.25 2.25 + 3x + x2 = 28.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 1.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 1.5 = 5.315072906 Simplifying x + 1.5 = 5.315072906 Reorder the terms: 1.5 + x = 5.315072906 Solving 1.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.315072906 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.315072906 + -1.5 x = 5.315072906 + -1.5 Combine like terms: 5.315072906 + -1.5 = 3.815072906 x = 3.815072906 Simplifying x = 3.815072906Subproblem 2
x + 1.5 = -5.315072906 Simplifying x + 1.5 = -5.315072906 Reorder the terms: 1.5 + x = -5.315072906 Solving 1.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.315072906 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.315072906 + -1.5 x = -5.315072906 + -1.5 Combine like terms: -5.315072906 + -1.5 = -6.815072906 x = -6.815072906 Simplifying x = -6.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.815072906, -6.815072906}
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