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Simplifying (x + 3)(x + -5) = 6 Reorder the terms: (3 + x)(x + -5) = 6 Reorder the terms: (3 + x)(-5 + x) = 6 Multiply (3 + x) * (-5 + x) (3(-5 + x) + x(-5 + x)) = 6 ((-5 * 3 + x * 3) + x(-5 + x)) = 6 ((-15 + 3x) + x(-5 + x)) = 6 (-15 + 3x + (-5 * x + x * x)) = 6 (-15 + 3x + (-5x + x2)) = 6 Combine like terms: 3x + -5x = -2x (-15 + -2x + x2) = 6 Solving -15 + -2x + x2 = 6 Solving for variable 'x'. Reorder the terms: -15 + -6 + -2x + x2 = 6 + -6 Combine like terms: -15 + -6 = -21 -21 + -2x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -21 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -2x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -2x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2x + x2 = 0 + 21 -2x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2x + x2 = 21 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 = 21 + 1 Reorder the terms: 1 + -2x + x2 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + -2x + x2 = 22 Factor a perfect square on the left side: (x + -1)(x + -1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -1) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -1 = 4.69041576 Simplifying x + -1 = 4.69041576 Reorder the terms: -1 + x = 4.69041576 Solving -1 + x = 4.69041576 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 = 4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.69041576 + 1 x = 4.69041576 + 1 Combine like terms: 4.69041576 + 1 = 5.69041576 x = 5.69041576 Simplifying x = 5.69041576Subproblem 2
x + -1 = -4.69041576 Simplifying x + -1 = -4.69041576 Reorder the terms: -1 + x = -4.69041576 Solving -1 + x = -4.69041576 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 = -4.69041576 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.69041576 + 1 x = -4.69041576 + 1 Combine like terms: -4.69041576 + 1 = -3.69041576 x = -3.69041576 Simplifying x = -3.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.69041576, -3.69041576}
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