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Simplifying (x + 5)(x + -1) = 5 Reorder the terms: (5 + x)(x + -1) = 5 Reorder the terms: (5 + x)(-1 + x) = 5 Multiply (5 + x) * (-1 + x) (5(-1 + x) + x(-1 + x)) = 5 ((-1 * 5 + x * 5) + x(-1 + x)) = 5 ((-5 + 5x) + x(-1 + x)) = 5 (-5 + 5x + (-1 * x + x * x)) = 5 (-5 + 5x + (-1x + x2)) = 5 Combine like terms: 5x + -1x = 4x (-5 + 4x + x2) = 5 Solving -5 + 4x + x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -5 + 4x + x2 = 5 + -5 Combine like terms: -5 + -5 = -10 -10 + 4x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -10 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4x + x2 = 0 + 10 4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 4x + x2 = 10 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 = 10 + 4 Reorder the terms: 4 + 4x + x2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + 4x + x2 = 14 Factor a perfect square on the left side: (x + 2)(x + 2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 2) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 2 = 3.741657387 Simplifying x + 2 = 3.741657387 Reorder the terms: 2 + x = 3.741657387 Solving 2 + x = 3.741657387 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 = 3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.741657387 + -2 x = 3.741657387 + -2 Combine like terms: 3.741657387 + -2 = 1.741657387 x = 1.741657387 Simplifying x = 1.741657387Subproblem 2
x + 2 = -3.741657387 Simplifying x + 2 = -3.741657387 Reorder the terms: 2 + x = -3.741657387 Solving 2 + x = -3.741657387 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 = -3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.741657387 + -2 x = -3.741657387 + -2 Combine like terms: -3.741657387 + -2 = -5.741657387 x = -5.741657387 Simplifying x = -5.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.741657387, -5.741657387}
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