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Simplifying (2x + 6)(2x + 6) = 108 Reorder the terms: (6 + 2x)(2x + 6) = 108 Reorder the terms: (6 + 2x)(6 + 2x) = 108 Multiply (6 + 2x) * (6 + 2x) (6(6 + 2x) + 2x * (6 + 2x)) = 108 ((6 * 6 + 2x * 6) + 2x * (6 + 2x)) = 108 ((36 + 12x) + 2x * (6 + 2x)) = 108 (36 + 12x + (6 * 2x + 2x * 2x)) = 108 (36 + 12x + (12x + 4x2)) = 108 Combine like terms: 12x + 12x = 24x (36 + 24x + 4x2) = 108 Solving 36 + 24x + 4x2 = 108 Solving for variable 'x'. Reorder the terms: 36 + -108 + 24x + 4x2 = 108 + -108 Combine like terms: 36 + -108 = -72 -72 + 24x + 4x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -72 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-18 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-18 + 6x + x2)' equal to zero and attempt to solve: Simplifying -18 + 6x + x2 = 0 Solving -18 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6x + x2 = 0 + 18 6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 6x + x2 = 18 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 18 + 9 Reorder the terms: 9 + 6x + x2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + 6x + x2 = 27 Factor a perfect square on the left side: (x + 3)(x + 3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 3) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 3 = 5.196152423 Simplifying x + 3 = 5.196152423 Reorder the terms: 3 + x = 5.196152423 Solving 3 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.196152423 + -3 x = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 x = 2.196152423 Simplifying x = 2.196152423Subproblem 2
x + 3 = -5.196152423 Simplifying x + 3 = -5.196152423 Reorder the terms: 3 + x = -5.196152423 Solving 3 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.196152423 + -3 x = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 x = -8.196152423 Simplifying x = -8.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.196152423, -8.196152423}Solution
x = {2.196152423, -8.196152423}
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