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Simplifying (x + -6)(x + 2) = 24 Reorder the terms: (-6 + x)(x + 2) = 24 Reorder the terms: (-6 + x)(2 + x) = 24 Multiply (-6 + x) * (2 + x) (-6(2 + x) + x(2 + x)) = 24 ((2 * -6 + x * -6) + x(2 + x)) = 24 ((-12 + -6x) + x(2 + x)) = 24 (-12 + -6x + (2 * x + x * x)) = 24 (-12 + -6x + (2x + x2)) = 24 Combine like terms: -6x + 2x = -4x (-12 + -4x + x2) = 24 Solving -12 + -4x + x2 = 24 Solving for variable 'x'. Reorder the terms: -12 + -24 + -4x + x2 = 24 + -24 Combine like terms: -12 + -24 = -36 -36 + -4x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -36 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -4x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -4x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -4x + x2 = 0 + 36 -4x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -4x + x2 = 36 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 = 36 + 4 Reorder the terms: 4 + -4x + x2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + -4x + x2 = 40 Factor a perfect square on the left side: (x + -2)(x + -2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -2) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -2 = 6.32455532 Simplifying x + -2 = 6.32455532 Reorder the terms: -2 + x = 6.32455532 Solving -2 + x = 6.32455532 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 = 6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.32455532 + 2 x = 6.32455532 + 2 Combine like terms: 6.32455532 + 2 = 8.32455532 x = 8.32455532 Simplifying x = 8.32455532Subproblem 2
x + -2 = -6.32455532 Simplifying x + -2 = -6.32455532 Reorder the terms: -2 + x = -6.32455532 Solving -2 + x = -6.32455532 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 = -6.32455532 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.32455532 + 2 x = -6.32455532 + 2 Combine like terms: -6.32455532 + 2 = -4.32455532 x = -4.32455532 Simplifying x = -4.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.32455532, -4.32455532}
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