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Simplifying (x + -2)(x + -3) = (x + 9) Reorder the terms: (-2 + x)(x + -3) = (x + 9) Reorder the terms: (-2 + x)(-3 + x) = (x + 9) Multiply (-2 + x) * (-3 + x) (-2(-3 + x) + x(-3 + x)) = (x + 9) ((-3 * -2 + x * -2) + x(-3 + x)) = (x + 9) ((6 + -2x) + x(-3 + x)) = (x + 9) (6 + -2x + (-3 * x + x * x)) = (x + 9) (6 + -2x + (-3x + x2)) = (x + 9) Combine like terms: -2x + -3x = -5x (6 + -5x + x2) = (x + 9) Reorder the terms: 6 + -5x + x2 = (9 + x) Remove parenthesis around (9 + x) 6 + -5x + x2 = 9 + x Solving 6 + -5x + x2 = 9 + x Solving for variable 'x'. Reorder the terms: 6 + -9 + -5x + -1x + x2 = 9 + x + -9 + -1x Combine like terms: 6 + -9 = -3 -3 + -5x + -1x + x2 = 9 + x + -9 + -1x Combine like terms: -5x + -1x = -6x -3 + -6x + x2 = 9 + x + -9 + -1x Reorder the terms: -3 + -6x + x2 = 9 + -9 + x + -1x Combine like terms: 9 + -9 = 0 -3 + -6x + x2 = 0 + x + -1x -3 + -6x + x2 = x + -1x Combine like terms: x + -1x = 0 -3 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6x + x2 = 0 + 3 -6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6x + x2 = 3 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 3 + 9 Reorder the terms: 9 + -6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6x + x2 = 12 Factor a perfect square on the left side: (x + -3)(x + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -3 = 3.464101615 Simplifying x + -3 = 3.464101615 Reorder the terms: -3 + x = 3.464101615 Solving -3 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.464101615 + 3 x = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 x = 6.464101615 Simplifying x = 6.464101615Subproblem 2
x + -3 = -3.464101615 Simplifying x + -3 = -3.464101615 Reorder the terms: -3 + x = -3.464101615 Solving -3 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.464101615 + 3 x = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 x = -0.464101615 Simplifying x = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.464101615, -0.464101615}
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