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Simplifying (x + 1)(x + -6) = 1 Reorder the terms: (1 + x)(x + -6) = 1 Reorder the terms: (1 + x)(-6 + x) = 1 Multiply (1 + x) * (-6 + x) (1(-6 + x) + x(-6 + x)) = 1 ((-6 * 1 + x * 1) + x(-6 + x)) = 1 ((-6 + 1x) + x(-6 + x)) = 1 (-6 + 1x + (-6 * x + x * x)) = 1 (-6 + 1x + (-6x + x2)) = 1 Combine like terms: 1x + -6x = -5x (-6 + -5x + x2) = 1 Solving -6 + -5x + x2 = 1 Solving for variable 'x'. Reorder the terms: -6 + -1 + -5x + x2 = 1 + -1 Combine like terms: -6 + -1 = -7 -7 + -5x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -7 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x + x2 = 0 + 7 -5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5x + x2 = 7 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 7 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + -5x + x2 = 13.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -2.5 = 3.640054945 Simplifying x + -2.5 = 3.640054945 Reorder the terms: -2.5 + x = 3.640054945 Solving -2.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.640054945 + 2.5 x = 3.640054945 + 2.5 Combine like terms: 3.640054945 + 2.5 = 6.140054945 x = 6.140054945 Simplifying x = 6.140054945Subproblem 2
x + -2.5 = -3.640054945 Simplifying x + -2.5 = -3.640054945 Reorder the terms: -2.5 + x = -3.640054945 Solving -2.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.640054945 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.640054945 + 2.5 x = -3.640054945 + 2.5 Combine like terms: -3.640054945 + 2.5 = -1.140054945 x = -1.140054945 Simplifying x = -1.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.140054945, -1.140054945}
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