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Simplifying (x + 9)(x + -5) = (x + 1) * 2 Reorder the terms: (9 + x)(x + -5) = (x + 1) * 2 Reorder the terms: (9 + x)(-5 + x) = (x + 1) * 2 Multiply (9 + x) * (-5 + x) (9(-5 + x) + x(-5 + x)) = (x + 1) * 2 ((-5 * 9 + x * 9) + x(-5 + x)) = (x + 1) * 2 ((-45 + 9x) + x(-5 + x)) = (x + 1) * 2 (-45 + 9x + (-5 * x + x * x)) = (x + 1) * 2 (-45 + 9x + (-5x + x2)) = (x + 1) * 2 Combine like terms: 9x + -5x = 4x (-45 + 4x + x2) = (x + 1) * 2 Reorder the terms: -45 + 4x + x2 = (1 + x) * 2 Reorder the terms for easier multiplication: -45 + 4x + x2 = 2(1 + x) -45 + 4x + x2 = (1 * 2 + x * 2) -45 + 4x + x2 = (2 + 2x) Solving -45 + 4x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -45 + -2 + 4x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -45 + -2 = -47 -47 + 4x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: 4x + -2x = 2x -47 + 2x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -47 + 2x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -47 + 2x + x2 = 0 + 2x + -2x -47 + 2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -47 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 2x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2x + x2 = 0 + 47 2x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 2x + x2 = 47 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 = 47 + 1 Reorder the terms: 1 + 2x + x2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2x + x2 = 48 Factor a perfect square on the left side: (x + 1)(x + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 1 = 6.92820323 Simplifying x + 1 = 6.92820323 Reorder the terms: 1 + x = 6.92820323 Solving 1 + x = 6.92820323 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 = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.92820323 + -1 x = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 x = 5.92820323 Simplifying x = 5.92820323Subproblem 2
x + 1 = -6.92820323 Simplifying x + 1 = -6.92820323 Reorder the terms: 1 + x = -6.92820323 Solving 1 + x = -6.92820323 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 = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.92820323 + -1 x = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 x = -7.92820323 Simplifying x = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.92820323, -7.92820323}
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