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Simplifying (x + 1)(x + -5) = 12 Reorder the terms: (1 + x)(x + -5) = 12 Reorder the terms: (1 + x)(-5 + x) = 12 Multiply (1 + x) * (-5 + x) (1(-5 + x) + x(-5 + x)) = 12 ((-5 * 1 + x * 1) + x(-5 + x)) = 12 ((-5 + 1x) + x(-5 + x)) = 12 (-5 + 1x + (-5 * x + x * x)) = 12 (-5 + 1x + (-5x + x2)) = 12 Combine like terms: 1x + -5x = -4x (-5 + -4x + x2) = 12 Solving -5 + -4x + x2 = 12 Solving for variable 'x'. Reorder the terms: -5 + -12 + -4x + x2 = 12 + -12 Combine like terms: -5 + -12 = -17 -17 + -4x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -17 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -4x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -4x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -4x + x2 = 0 + 17 -4x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -4x + x2 = 17 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 = 17 + 4 Reorder the terms: 4 + -4x + x2 = 17 + 4 Combine like terms: 17 + 4 = 21 4 + -4x + x2 = 21 Factor a perfect square on the left side: (x + -2)(x + -2) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -2) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -2 = 4.582575695 Simplifying x + -2 = 4.582575695 Reorder the terms: -2 + x = 4.582575695 Solving -2 + x = 4.582575695 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 = 4.582575695 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.582575695 + 2 x = 4.582575695 + 2 Combine like terms: 4.582575695 + 2 = 6.582575695 x = 6.582575695 Simplifying x = 6.582575695Subproblem 2
x + -2 = -4.582575695 Simplifying x + -2 = -4.582575695 Reorder the terms: -2 + x = -4.582575695 Solving -2 + x = -4.582575695 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 = -4.582575695 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.582575695 + 2 x = -4.582575695 + 2 Combine like terms: -4.582575695 + 2 = -2.582575695 x = -2.582575695 Simplifying x = -2.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.582575695, -2.582575695}
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