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Simplifying (x + -1)(x + -5) = 7 Reorder the terms: (-1 + x)(x + -5) = 7 Reorder the terms: (-1 + x)(-5 + x) = 7 Multiply (-1 + x) * (-5 + x) (-1(-5 + x) + x(-5 + x)) = 7 ((-5 * -1 + x * -1) + x(-5 + x)) = 7 ((5 + -1x) + x(-5 + x)) = 7 (5 + -1x + (-5 * x + x * x)) = 7 (5 + -1x + (-5x + x2)) = 7 Combine like terms: -1x + -5x = -6x (5 + -6x + x2) = 7 Solving 5 + -6x + x2 = 7 Solving for variable 'x'. Reorder the terms: 5 + -7 + -6x + x2 = 7 + -7 Combine like terms: 5 + -7 = -2 -2 + -6x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -2 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6x + x2 = 0 + 2 -6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6x + x2 = 2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + -6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6x + x2 = 11 Factor a perfect square on the left side: (x + -3)(x + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -3 = 3.31662479 Simplifying x + -3 = 3.31662479 Reorder the terms: -3 + x = 3.31662479 Solving -3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.31662479 + 3 x = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 x = 6.31662479 Simplifying x = 6.31662479Subproblem 2
x + -3 = -3.31662479 Simplifying x + -3 = -3.31662479 Reorder the terms: -3 + x = -3.31662479 Solving -3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.31662479 + 3 x = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 x = -0.31662479 Simplifying x = -0.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.31662479, -0.31662479}
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