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Simplifying (x + -3)(x + -3) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 Reorder the terms: (-3 + x)(x + -3) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 Reorder the terms: (-3 + x)(-3 + x) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 ((-3 * -3 + x * -3) + x(-3 + x)) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 ((9 + -3x) + x(-3 + x)) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 (9 + -3x + (-3 * x + x * x)) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 (9 + -3x + (-3x + x2)) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) + -1(x + 2)(x + 2) + -2(x + -3)(x + 2) = 0 Reorder the terms: 9 + -6x + x2 + -1(2 + x)(x + 2) + -2(x + -3)(x + 2) = 0 Reorder the terms: 9 + -6x + x2 + -1(2 + x)(2 + x) + -2(x + -3)(x + 2) = 0 Multiply (2 + x) * (2 + x) 9 + -6x + x2 + -1(2(2 + x) + x(2 + x)) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + -1((2 * 2 + x * 2) + x(2 + x)) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + -1((4 + 2x) + x(2 + x)) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + -1(4 + 2x + (2 * x + x * x)) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + -1(4 + 2x + (2x + x2)) + -2(x + -3)(x + 2) = 0 Combine like terms: 2x + 2x = 4x 9 + -6x + x2 + -1(4 + 4x + x2) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + (4 * -1 + 4x * -1 + x2 * -1) + -2(x + -3)(x + 2) = 0 9 + -6x + x2 + (-4 + -4x + -1x2) + -2(x + -3)(x + 2) = 0 Reorder the terms: 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-3 + x)(x + 2) = 0 Reorder the terms: 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-3 + x)(2 + x) = 0 Multiply (-3 + x) * (2 + x) 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-3(2 + x) + x(2 + x)) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + -2((2 * -3 + x * -3) + x(2 + x)) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + -2((-6 + -3x) + x(2 + x)) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-6 + -3x + (2 * x + x * x)) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-6 + -3x + (2x + x2)) = 0 Combine like terms: -3x + 2x = -1x 9 + -6x + x2 + -4 + -4x + -1x2 + -2(-6 + -1x + x2) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + (-6 * -2 + -1x * -2 + x2 * -2) = 0 9 + -6x + x2 + -4 + -4x + -1x2 + (12 + 2x + -2x2) = 0 Reorder the terms: 9 + -4 + 12 + -6x + -4x + 2x + x2 + -1x2 + -2x2 = 0 Combine like terms: 9 + -4 = 5 5 + 12 + -6x + -4x + 2x + x2 + -1x2 + -2x2 = 0 Combine like terms: 5 + 12 = 17 17 + -6x + -4x + 2x + x2 + -1x2 + -2x2 = 0 Combine like terms: -6x + -4x = -10x 17 + -10x + 2x + x2 + -1x2 + -2x2 = 0 Combine like terms: -10x + 2x = -8x 17 + -8x + x2 + -1x2 + -2x2 = 0 Combine like terms: x2 + -1x2 = 0 17 + -8x + 0 + -2x2 = 0 17 + -8x + -2x2 = 0 Solving 17 + -8x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8.5 + 4x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 4x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 4x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 4x + x2 = 0 + 8.5 4x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 4x + x2 = 8.5 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 = 8.5 + 4 Reorder the terms: 4 + 4x + x2 = 8.5 + 4 Combine like terms: 8.5 + 4 = 12.5 4 + 4x + x2 = 12.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 2) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 2 = 3.535533906 Simplifying x + 2 = 3.535533906 Reorder the terms: 2 + x = 3.535533906 Solving 2 + x = 3.535533906 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 = 3.535533906 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.535533906 + -2 x = 3.535533906 + -2 Combine like terms: 3.535533906 + -2 = 1.535533906 x = 1.535533906 Simplifying x = 1.535533906Subproblem 2
x + 2 = -3.535533906 Simplifying x + 2 = -3.535533906 Reorder the terms: 2 + x = -3.535533906 Solving 2 + x = -3.535533906 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 = -3.535533906 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.535533906 + -2 x = -3.535533906 + -2 Combine like terms: -3.535533906 + -2 = -5.535533906 x = -5.535533906 Simplifying x = -5.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.535533906, -5.535533906}
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