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Simplifying (2x + 4)(2x + 2) = 272 Reorder the terms: (4 + 2x)(2x + 2) = 272 Reorder the terms: (4 + 2x)(2 + 2x) = 272 Multiply (4 + 2x) * (2 + 2x) (4(2 + 2x) + 2x * (2 + 2x)) = 272 ((2 * 4 + 2x * 4) + 2x * (2 + 2x)) = 272 ((8 + 8x) + 2x * (2 + 2x)) = 272 (8 + 8x + (2 * 2x + 2x * 2x)) = 272 (8 + 8x + (4x + 4x2)) = 272 Combine like terms: 8x + 4x = 12x (8 + 12x + 4x2) = 272 Solving 8 + 12x + 4x2 = 272 Solving for variable 'x'. Reorder the terms: 8 + -272 + 12x + 4x2 = 272 + -272 Combine like terms: 8 + -272 = -264 -264 + 12x + 4x2 = 272 + -272 Combine like terms: 272 + -272 = 0 -264 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-66 + 3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-66 + 3x + x2)' equal to zero and attempt to solve: Simplifying -66 + 3x + x2 = 0 Solving -66 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 3x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 3x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 3x + x2 = 0 + 66 3x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 3x + x2 = 66 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 = 66 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 66 + 2.25 Combine like terms: 66 + 2.25 = 68.25 2.25 + 3x + x2 = 68.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 1.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 1.5 = 8.261355821 Simplifying x + 1.5 = 8.261355821 Reorder the terms: 1.5 + x = 8.261355821 Solving 1.5 + x = 8.261355821 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 = 8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.261355821 + -1.5 x = 8.261355821 + -1.5 Combine like terms: 8.261355821 + -1.5 = 6.761355821 x = 6.761355821 Simplifying x = 6.761355821Subproblem 2
x + 1.5 = -8.261355821 Simplifying x + 1.5 = -8.261355821 Reorder the terms: 1.5 + x = -8.261355821 Solving 1.5 + x = -8.261355821 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 = -8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.261355821 + -1.5 x = -8.261355821 + -1.5 Combine like terms: -8.261355821 + -1.5 = -9.761355821 x = -9.761355821 Simplifying x = -9.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.761355821, -9.761355821}Solution
x = {6.761355821, -9.761355821}
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