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Simplifying (x + -1)(x + 5) = 3 Reorder the terms: (-1 + x)(x + 5) = 3 Reorder the terms: (-1 + x)(5 + x) = 3 Multiply (-1 + x) * (5 + x) (-1(5 + x) + x(5 + x)) = 3 ((5 * -1 + x * -1) + x(5 + x)) = 3 ((-5 + -1x) + x(5 + x)) = 3 (-5 + -1x + (5 * x + x * x)) = 3 (-5 + -1x + (5x + x2)) = 3 Combine like terms: -1x + 5x = 4x (-5 + 4x + x2) = 3 Solving -5 + 4x + x2 = 3 Solving for variable 'x'. Reorder the terms: -5 + -3 + 4x + x2 = 3 + -3 Combine like terms: -5 + -3 = -8 -8 + 4x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -8 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4x + x2 = 0 + 8 4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 4x + x2 = 8 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 = 8 + 4 Reorder the terms: 4 + 4x + x2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4x + x2 = 12 Factor a perfect square on the left side: (x + 2)(x + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 2 = 3.464101615 Simplifying x + 2 = 3.464101615 Reorder the terms: 2 + x = 3.464101615 Solving 2 + x = 3.464101615 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 = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.464101615 + -2 x = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 x = 1.464101615 Simplifying x = 1.464101615Subproblem 2
x + 2 = -3.464101615 Simplifying x + 2 = -3.464101615 Reorder the terms: 2 + x = -3.464101615 Solving 2 + x = -3.464101615 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 = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.464101615 + -2 x = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 x = -5.464101615 Simplifying x = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.464101615, -5.464101615}
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