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Simplifying (x + 2)(x + -3) = ((x + 3) * 2) Reorder the terms: (2 + x)(x + -3) = ((x + 3) * 2) Reorder the terms: (2 + x)(-3 + x) = ((x + 3) * 2) Multiply (2 + x) * (-3 + x) (2(-3 + x) + x(-3 + x)) = ((x + 3) * 2) ((-3 * 2 + x * 2) + x(-3 + x)) = ((x + 3) * 2) ((-6 + 2x) + x(-3 + x)) = ((x + 3) * 2) (-6 + 2x + (-3 * x + x * x)) = ((x + 3) * 2) (-6 + 2x + (-3x + x2)) = ((x + 3) * 2) Combine like terms: 2x + -3x = -1x (-6 + -1x + x2) = ((x + 3) * 2) Reorder the terms: -6 + -1x + x2 = ((3 + x) * 2) Reorder the terms for easier multiplication: -6 + -1x + x2 = (2(3 + x)) -6 + -1x + x2 = ((3 * 2 + x * 2)) -6 + -1x + x2 = ((6 + 2x)) -6 + -1x + x2 = (6 + 2x) Remove parenthesis around (6 + 2x) -6 + -1x + x2 = 6 + 2x Solving -6 + -1x + x2 = 6 + 2x Solving for variable 'x'. Reorder the terms: -6 + -6 + -1x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: -6 + -6 = -12 -12 + -1x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: -1x + -2x = -3x -12 + -3x + x2 = 6 + 2x + -6 + -2x Reorder the terms: -12 + -3x + x2 = 6 + -6 + 2x + -2x Combine like terms: 6 + -6 = 0 -12 + -3x + x2 = 0 + 2x + -2x -12 + -3x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -12 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -3x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -3x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3x + x2 = 0 + 12 -3x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3x + x2 = 12 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 12 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 12 + 2.25 Combine like terms: 12 + 2.25 = 14.25 2.25 + -3x + x2 = 14.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -1.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -1.5 = 3.774917218 Simplifying x + -1.5 = 3.774917218 Reorder the terms: -1.5 + x = 3.774917218 Solving -1.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.774917218 + 1.5 x = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 x = 5.274917218 Simplifying x = 5.274917218Subproblem 2
x + -1.5 = -3.774917218 Simplifying x + -1.5 = -3.774917218 Reorder the terms: -1.5 + x = -3.774917218 Solving -1.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.774917218 + 1.5 x = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 x = -2.274917218 Simplifying x = -2.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.274917218, -2.274917218}
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