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Simplifying (x + 5)(x + -1) = (x + 1) * 2 Reorder the terms: (5 + x)(x + -1) = (x + 1) * 2 Reorder the terms: (5 + x)(-1 + x) = (x + 1) * 2 Multiply (5 + x) * (-1 + x) (5(-1 + x) + x(-1 + x)) = (x + 1) * 2 ((-1 * 5 + x * 5) + x(-1 + x)) = (x + 1) * 2 ((-5 + 5x) + x(-1 + x)) = (x + 1) * 2 (-5 + 5x + (-1 * x + x * x)) = (x + 1) * 2 (-5 + 5x + (-1x + x2)) = (x + 1) * 2 Combine like terms: 5x + -1x = 4x (-5 + 4x + x2) = (x + 1) * 2 Reorder the terms: -5 + 4x + x2 = (1 + x) * 2 Reorder the terms for easier multiplication: -5 + 4x + x2 = 2(1 + x) -5 + 4x + x2 = (1 * 2 + x * 2) -5 + 4x + x2 = (2 + 2x) Solving -5 + 4x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -5 + -2 + 4x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -5 + -2 = -7 -7 + 4x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: 4x + -2x = 2x -7 + 2x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -7 + 2x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -7 + 2x + x2 = 0 + 2x + -2x -7 + 2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -7 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x + x2 = 0 + 7 2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 2x + x2 = 7 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 7 + 1 Reorder the terms: 1 + 2x + x2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2x + x2 = 8 Factor a perfect square on the left side: (x + 1)(x + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 1 = 2.828427125 Simplifying x + 1 = 2.828427125 Reorder the terms: 1 + x = 2.828427125 Solving 1 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.828427125 + -1 x = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 x = 1.828427125 Simplifying x = 1.828427125Subproblem 2
x + 1 = -2.828427125 Simplifying x + 1 = -2.828427125 Reorder the terms: 1 + x = -2.828427125 Solving 1 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.828427125 + -1 x = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 x = -3.828427125 Simplifying x = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.828427125, -3.828427125}
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