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Simplifying (x + -2)(x + 5) = 9 Reorder the terms: (-2 + x)(x + 5) = 9 Reorder the terms: (-2 + x)(5 + x) = 9 Multiply (-2 + x) * (5 + x) (-2(5 + x) + x(5 + x)) = 9 ((5 * -2 + x * -2) + x(5 + x)) = 9 ((-10 + -2x) + x(5 + x)) = 9 (-10 + -2x + (5 * x + x * x)) = 9 (-10 + -2x + (5x + x2)) = 9 Combine like terms: -2x + 5x = 3x (-10 + 3x + x2) = 9 Solving -10 + 3x + x2 = 9 Solving for variable 'x'. Reorder the terms: -10 + -9 + 3x + x2 = 9 + -9 Combine like terms: -10 + -9 = -19 -19 + 3x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -19 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 3x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 3x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 3x + x2 = 0 + 19 3x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 3x + x2 = 19 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 = 19 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 19 + 2.25 Combine like terms: 19 + 2.25 = 21.25 2.25 + 3x + x2 = 21.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 1.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 1.5 = 4.609772229 Simplifying x + 1.5 = 4.609772229 Reorder the terms: 1.5 + x = 4.609772229 Solving 1.5 + x = 4.609772229 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 = 4.609772229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.609772229 + -1.5 x = 4.609772229 + -1.5 Combine like terms: 4.609772229 + -1.5 = 3.109772229 x = 3.109772229 Simplifying x = 3.109772229Subproblem 2
x + 1.5 = -4.609772229 Simplifying x + 1.5 = -4.609772229 Reorder the terms: 1.5 + x = -4.609772229 Solving 1.5 + x = -4.609772229 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 = -4.609772229 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.609772229 + -1.5 x = -4.609772229 + -1.5 Combine like terms: -4.609772229 + -1.5 = -6.109772229 x = -6.109772229 Simplifying x = -6.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.109772229, -6.109772229}
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