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Simplifying (2x + 8)(x + -6) + 3(x + -2) = 0 Reorder the terms: (8 + 2x)(x + -6) + 3(x + -2) = 0 Reorder the terms: (8 + 2x)(-6 + x) + 3(x + -2) = 0 Multiply (8 + 2x) * (-6 + x) (8(-6 + x) + 2x * (-6 + x)) + 3(x + -2) = 0 ((-6 * 8 + x * 8) + 2x * (-6 + x)) + 3(x + -2) = 0 ((-48 + 8x) + 2x * (-6 + x)) + 3(x + -2) = 0 (-48 + 8x + (-6 * 2x + x * 2x)) + 3(x + -2) = 0 (-48 + 8x + (-12x + 2x2)) + 3(x + -2) = 0 Combine like terms: 8x + -12x = -4x (-48 + -4x + 2x2) + 3(x + -2) = 0 Reorder the terms: -48 + -4x + 2x2 + 3(-2 + x) = 0 -48 + -4x + 2x2 + (-2 * 3 + x * 3) = 0 -48 + -4x + 2x2 + (-6 + 3x) = 0 Reorder the terms: -48 + -6 + -4x + 3x + 2x2 = 0 Combine like terms: -48 + -6 = -54 -54 + -4x + 3x + 2x2 = 0 Combine like terms: -4x + 3x = -1x -54 + -1x + 2x2 = 0 Solving -54 + -1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27 + -0.5x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -0.5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -0.5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -0.5x + x2 = 0 + 27 -0.5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -0.5x + x2 = 27 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 27 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 27 + 0.0625 Combine like terms: 27 + 0.0625 = 27.0625 0.0625 + -0.5x + x2 = 27.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (x + -0.25) equal to 5.202163012 and -5.202163012.Subproblem 1
x + -0.25 = 5.202163012 Simplifying x + -0.25 = 5.202163012 Reorder the terms: -0.25 + x = 5.202163012 Solving -0.25 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.202163012 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.202163012 + 0.25 x = 5.202163012 + 0.25 Combine like terms: 5.202163012 + 0.25 = 5.452163012 x = 5.452163012 Simplifying x = 5.452163012Subproblem 2
x + -0.25 = -5.202163012 Simplifying x + -0.25 = -5.202163012 Reorder the terms: -0.25 + x = -5.202163012 Solving -0.25 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.202163012 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.202163012 + 0.25 x = -5.202163012 + 0.25 Combine like terms: -5.202163012 + 0.25 = -4.952163012 x = -4.952163012 Simplifying x = -4.952163012Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.452163012, -4.952163012}
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