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Simplifying (x + -3)(x + -2) = (x + -2) * 2 + -1 Reorder the terms: (-3 + x)(x + -2) = (x + -2) * 2 + -1 Reorder the terms: (-3 + x)(-2 + x) = (x + -2) * 2 + -1 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = (x + -2) * 2 + -1 ((-2 * -3 + x * -3) + x(-2 + x)) = (x + -2) * 2 + -1 ((6 + -3x) + x(-2 + x)) = (x + -2) * 2 + -1 (6 + -3x + (-2 * x + x * x)) = (x + -2) * 2 + -1 (6 + -3x + (-2x + x2)) = (x + -2) * 2 + -1 Combine like terms: -3x + -2x = -5x (6 + -5x + x2) = (x + -2) * 2 + -1 Reorder the terms: 6 + -5x + x2 = (-2 + x) * 2 + -1 Reorder the terms for easier multiplication: 6 + -5x + x2 = 2(-2 + x) + -1 6 + -5x + x2 = (-2 * 2 + x * 2) + -1 6 + -5x + x2 = (-4 + 2x) + -1 Reorder the terms: 6 + -5x + x2 = -4 + -1 + 2x Combine like terms: -4 + -1 = -5 6 + -5x + x2 = -5 + 2x Solving 6 + -5x + x2 = -5 + 2x Solving for variable 'x'. Reorder the terms: 6 + 5 + -5x + -2x + x2 = -5 + 2x + 5 + -2x Combine like terms: 6 + 5 = 11 11 + -5x + -2x + x2 = -5 + 2x + 5 + -2x Combine like terms: -5x + -2x = -7x 11 + -7x + x2 = -5 + 2x + 5 + -2x Reorder the terms: 11 + -7x + x2 = -5 + 5 + 2x + -2x Combine like terms: -5 + 5 = 0 11 + -7x + x2 = 0 + 2x + -2x 11 + -7x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 11 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -7x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x + x2 = 0 + -11 -7x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7x + x2 = -11 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -11 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -11 + 12.25 Combine like terms: -11 + 12.25 = 1.25 12.25 + -7x + x2 = 1.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -3.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -3.5 = 1.118033989 Simplifying x + -3.5 = 1.118033989 Reorder the terms: -3.5 + x = 1.118033989 Solving -3.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.118033989 + 3.5 x = 1.118033989 + 3.5 Combine like terms: 1.118033989 + 3.5 = 4.618033989 x = 4.618033989 Simplifying x = 4.618033989Subproblem 2
x + -3.5 = -1.118033989 Simplifying x + -3.5 = -1.118033989 Reorder the terms: -3.5 + x = -1.118033989 Solving -3.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.118033989 + 3.5 x = -1.118033989 + 3.5 Combine like terms: -1.118033989 + 3.5 = 2.381966011 x = 2.381966011 Simplifying x = 2.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.618033989, 2.381966011}
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