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Simplifying (x + 3)(2x + 4) = 20 Reorder the terms: (3 + x)(2x + 4) = 20 Reorder the terms: (3 + x)(4 + 2x) = 20 Multiply (3 + x) * (4 + 2x) (3(4 + 2x) + x(4 + 2x)) = 20 ((4 * 3 + 2x * 3) + x(4 + 2x)) = 20 ((12 + 6x) + x(4 + 2x)) = 20 (12 + 6x + (4 * x + 2x * x)) = 20 (12 + 6x + (4x + 2x2)) = 20 Combine like terms: 6x + 4x = 10x (12 + 10x + 2x2) = 20 Solving 12 + 10x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: 12 + -20 + 10x + 2x2 = 20 + -20 Combine like terms: 12 + -20 = -8 -8 + 10x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -8 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 5x + x2)' equal to zero and attempt to solve: Simplifying -4 + 5x + x2 = 0 Solving -4 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5x + x2 = 0 + 4 5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 5x + x2 = 4 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 4 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5x + x2 = 10.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + 2.5 = 3.201562119 Simplifying x + 2.5 = 3.201562119 Reorder the terms: 2.5 + x = 3.201562119 Solving 2.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.201562119 + -2.5 x = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 x = 0.701562119 Simplifying x = 0.701562119Subproblem 2
x + 2.5 = -3.201562119 Simplifying x + 2.5 = -3.201562119 Reorder the terms: 2.5 + x = -3.201562119 Solving 2.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.201562119 + -2.5 x = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 x = -5.701562119 Simplifying x = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701562119, -5.701562119}Solution
x = {0.701562119, -5.701562119}
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