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Simplifying (x + -3)(x + 3) + -1(2x + 9) * 2 = 0 Reorder the terms: (-3 + x)(x + 3) + -1(2x + 9) * 2 = 0 Reorder the terms: (-3 + x)(3 + x) + -1(2x + 9) * 2 = 0 Multiply (-3 + x) * (3 + x) (-3(3 + x) + x(3 + x)) + -1(2x + 9) * 2 = 0 ((3 * -3 + x * -3) + x(3 + x)) + -1(2x + 9) * 2 = 0 ((-9 + -3x) + x(3 + x)) + -1(2x + 9) * 2 = 0 (-9 + -3x + (3 * x + x * x)) + -1(2x + 9) * 2 = 0 (-9 + -3x + (3x + x2)) + -1(2x + 9) * 2 = 0 Combine like terms: -3x + 3x = 0 (-9 + 0 + x2) + -1(2x + 9) * 2 = 0 (-9 + x2) + -1(2x + 9) * 2 = 0 Reorder the terms: -9 + x2 + -1(9 + 2x) * 2 = 0 Reorder the terms for easier multiplication: -9 + x2 + -1 * 2(9 + 2x) = 0 Multiply -1 * 2 -9 + x2 + -2(9 + 2x) = 0 -9 + x2 + (9 * -2 + 2x * -2) = 0 -9 + x2 + (-18 + -4x) = 0 Reorder the terms: -9 + -18 + -4x + x2 = 0 Combine like terms: -9 + -18 = -27 -27 + -4x + x2 = 0 Solving -27 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -4x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -4x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -4x + x2 = 0 + 27 -4x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -4x + x2 = 27 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 = 27 + 4 Reorder the terms: 4 + -4x + x2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + -4x + x2 = 31 Factor a perfect square on the left side: (x + -2)(x + -2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -2) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -2 = 5.567764363 Simplifying x + -2 = 5.567764363 Reorder the terms: -2 + x = 5.567764363 Solving -2 + x = 5.567764363 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 = 5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.567764363 + 2 x = 5.567764363 + 2 Combine like terms: 5.567764363 + 2 = 7.567764363 x = 7.567764363 Simplifying x = 7.567764363Subproblem 2
x + -2 = -5.567764363 Simplifying x + -2 = -5.567764363 Reorder the terms: -2 + x = -5.567764363 Solving -2 + x = -5.567764363 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 = -5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.567764363 + 2 x = -5.567764363 + 2 Combine like terms: -5.567764363 + 2 = -3.567764363 x = -3.567764363 Simplifying x = -3.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.567764363, -3.567764363}
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