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Simplifying (2x + 6)(2x + 12) + -72 = 162 Reorder the terms: (6 + 2x)(2x + 12) + -72 = 162 Reorder the terms: (6 + 2x)(12 + 2x) + -72 = 162 Multiply (6 + 2x) * (12 + 2x) (6(12 + 2x) + 2x * (12 + 2x)) + -72 = 162 ((12 * 6 + 2x * 6) + 2x * (12 + 2x)) + -72 = 162 ((72 + 12x) + 2x * (12 + 2x)) + -72 = 162 (72 + 12x + (12 * 2x + 2x * 2x)) + -72 = 162 (72 + 12x + (24x + 4x2)) + -72 = 162 Combine like terms: 12x + 24x = 36x (72 + 36x + 4x2) + -72 = 162 Reorder the terms: 72 + -72 + 36x + 4x2 = 162 Combine like terms: 72 + -72 = 0 0 + 36x + 4x2 = 162 36x + 4x2 = 162 Solving 36x + 4x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + 36x + 4x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-81 + 18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-81 + 18x + 2x2)' equal to zero and attempt to solve: Simplifying -81 + 18x + 2x2 = 0 Solving -81 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 9x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 9x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 9x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 9x + x2 = 0 + 40.5 9x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 9x + x2 = 40.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 40.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 40.5 + 20.25 Combine like terms: 40.5 + 20.25 = 60.75 20.25 + 9x + x2 = 60.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 60.75 Calculate the square root of the right side: 7.794228634 Break this problem into two subproblems by setting (x + 4.5) equal to 7.794228634 and -7.794228634.Subproblem 1
x + 4.5 = 7.794228634 Simplifying x + 4.5 = 7.794228634 Reorder the terms: 4.5 + x = 7.794228634 Solving 4.5 + x = 7.794228634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 7.794228634 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.794228634 + -4.5 x = 7.794228634 + -4.5 Combine like terms: 7.794228634 + -4.5 = 3.294228634 x = 3.294228634 Simplifying x = 3.294228634Subproblem 2
x + 4.5 = -7.794228634 Simplifying x + 4.5 = -7.794228634 Reorder the terms: 4.5 + x = -7.794228634 Solving 4.5 + x = -7.794228634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -7.794228634 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.794228634 + -4.5 x = -7.794228634 + -4.5 Combine like terms: -7.794228634 + -4.5 = -12.294228634 x = -12.294228634 Simplifying x = -12.294228634Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.294228634, -12.294228634}Solution
x = {3.294228634, -12.294228634}
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