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Simplifying (x + 9)(x + -3) = (x + 1) * 2 Reorder the terms: (9 + x)(x + -3) = (x + 1) * 2 Reorder the terms: (9 + x)(-3 + x) = (x + 1) * 2 Multiply (9 + x) * (-3 + x) (9(-3 + x) + x(-3 + x)) = (x + 1) * 2 ((-3 * 9 + x * 9) + x(-3 + x)) = (x + 1) * 2 ((-27 + 9x) + x(-3 + x)) = (x + 1) * 2 (-27 + 9x + (-3 * x + x * x)) = (x + 1) * 2 (-27 + 9x + (-3x + x2)) = (x + 1) * 2 Combine like terms: 9x + -3x = 6x (-27 + 6x + x2) = (x + 1) * 2 Reorder the terms: -27 + 6x + x2 = (1 + x) * 2 Reorder the terms for easier multiplication: -27 + 6x + x2 = 2(1 + x) -27 + 6x + x2 = (1 * 2 + x * 2) -27 + 6x + x2 = (2 + 2x) Solving -27 + 6x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -27 + -2 + 6x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -27 + -2 = -29 -29 + 6x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: 6x + -2x = 4x -29 + 4x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -29 + 4x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -29 + 4x + x2 = 0 + 2x + -2x -29 + 4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -29 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 4x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 4x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 4x + x2 = 0 + 29 4x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 4x + x2 = 29 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 = 29 + 4 Reorder the terms: 4 + 4x + x2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + 4x + x2 = 33 Factor a perfect square on the left side: (x + 2)(x + 2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 2) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 2 = 5.744562647 Simplifying x + 2 = 5.744562647 Reorder the terms: 2 + x = 5.744562647 Solving 2 + x = 5.744562647 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 = 5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.744562647 + -2 x = 5.744562647 + -2 Combine like terms: 5.744562647 + -2 = 3.744562647 x = 3.744562647 Simplifying x = 3.744562647Subproblem 2
x + 2 = -5.744562647 Simplifying x + 2 = -5.744562647 Reorder the terms: 2 + x = -5.744562647 Solving 2 + x = -5.744562647 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 = -5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.744562647 + -2 x = -5.744562647 + -2 Combine like terms: -5.744562647 + -2 = -7.744562647 x = -7.744562647 Simplifying x = -7.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.744562647, -7.744562647}
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