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Simplifying (2x + 8)(x + 3) = 42 Reorder the terms: (8 + 2x)(x + 3) = 42 Reorder the terms: (8 + 2x)(3 + x) = 42 Multiply (8 + 2x) * (3 + x) (8(3 + x) + 2x * (3 + x)) = 42 ((3 * 8 + x * 8) + 2x * (3 + x)) = 42 ((24 + 8x) + 2x * (3 + x)) = 42 (24 + 8x + (3 * 2x + x * 2x)) = 42 (24 + 8x + (6x + 2x2)) = 42 Combine like terms: 8x + 6x = 14x (24 + 14x + 2x2) = 42 Solving 24 + 14x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: 24 + -42 + 14x + 2x2 = 42 + -42 Combine like terms: 24 + -42 = -18 -18 + 14x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -18 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 7x + x2)' equal to zero and attempt to solve: Simplifying -9 + 7x + x2 = 0 Solving -9 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 7x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 7x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7x + x2 = 0 + 9 7x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 7x + x2 = 9 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 = 9 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + 7x + x2 = 21.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 3.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 3.5 = 4.609772229 Simplifying x + 3.5 = 4.609772229 Reorder the terms: 3.5 + x = 4.609772229 Solving 3.5 + x = 4.609772229 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 = 4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.609772229 + -3.5 x = 4.609772229 + -3.5 Combine like terms: 4.609772229 + -3.5 = 1.109772229 x = 1.109772229 Simplifying x = 1.109772229Subproblem 2
x + 3.5 = -4.609772229 Simplifying x + 3.5 = -4.609772229 Reorder the terms: 3.5 + x = -4.609772229 Solving 3.5 + x = -4.609772229 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 = -4.609772229 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.609772229 + -3.5 x = -4.609772229 + -3.5 Combine like terms: -4.609772229 + -3.5 = -8.109772229 x = -8.109772229 Simplifying x = -8.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.109772229, -8.109772229}Solution
x = {1.109772229, -8.109772229}
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