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Simplifying (x + 2)(x + -3) = (x + 3) * 3 Reorder the terms: (2 + x)(x + -3) = (x + 3) * 3 Reorder the terms: (2 + x)(-3 + x) = (x + 3) * 3 Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = (x + 3) * 3 ((-3 * 2 + x * 2) + x(-3 + x)) = (x + 3) * 3 ((-6 + 2x) + x(-3 + x)) = (x + 3) * 3 (-6 + 2x + (-3 * x + x * x)) = (x + 3) * 3 (-6 + 2x + (-3x + x2)) = (x + 3) * 3 Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = (x + 3) * 3 Reorder the terms: -6 + -1x + x2 = (3 + x) * 3 Reorder the terms for easier multiplication: -6 + -1x + x2 = 3(3 + x) -6 + -1x + x2 = (3 * 3 + x * 3) -6 + -1x + x2 = (9 + 3x) Solving -6 + -1x + x2 = 9 + 3x Solving for variable 'x'. Reorder the terms: -6 + -9 + -1x + -3x + x2 = 9 + 3x + -9 + -3x Combine like terms: -6 + -9 = -15 -15 + -1x + -3x + x2 = 9 + 3x + -9 + -3x Combine like terms: -1x + -3x = -4x -15 + -4x + x2 = 9 + 3x + -9 + -3x Reorder the terms: -15 + -4x + x2 = 9 + -9 + 3x + -3x Combine like terms: 9 + -9 = 0 -15 + -4x + x2 = 0 + 3x + -3x -15 + -4x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -15 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4x + x2 = 0 + 15 -4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4x + x2 = 15 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 = 15 + 4 Reorder the terms: 4 + -4x + x2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4x + x2 = 19 Factor a perfect square on the left side: (x + -2)(x + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -2 = 4.358898944 Simplifying x + -2 = 4.358898944 Reorder the terms: -2 + x = 4.358898944 Solving -2 + x = 4.358898944 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 = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.358898944 + 2 x = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 x = 6.358898944 Simplifying x = 6.358898944Subproblem 2
x + -2 = -4.358898944 Simplifying x + -2 = -4.358898944 Reorder the terms: -2 + x = -4.358898944 Solving -2 + x = -4.358898944 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 = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.358898944 + 2 x = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 x = -2.358898944 Simplifying x = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.358898944, -2.358898944}
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