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Simplifying (2x + 12)(2x + 15) = 285 Reorder the terms: (12 + 2x)(2x + 15) = 285 Reorder the terms: (12 + 2x)(15 + 2x) = 285 Multiply (12 + 2x) * (15 + 2x) (12(15 + 2x) + 2x * (15 + 2x)) = 285 ((15 * 12 + 2x * 12) + 2x * (15 + 2x)) = 285 ((180 + 24x) + 2x * (15 + 2x)) = 285 (180 + 24x + (15 * 2x + 2x * 2x)) = 285 (180 + 24x + (30x + 4x2)) = 285 Combine like terms: 24x + 30x = 54x (180 + 54x + 4x2) = 285 Solving 180 + 54x + 4x2 = 285 Solving for variable 'x'. Reorder the terms: 180 + -285 + 54x + 4x2 = 285 + -285 Combine like terms: 180 + -285 = -105 -105 + 54x + 4x2 = 285 + -285 Combine like terms: 285 + -285 = 0 -105 + 54x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -26.25 + 13.5x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + 13.5x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + 13.5x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + 13.5x + x2 = 0 + 26.25 13.5x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 13.5x + x2 = 26.25 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 26.25 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 26.25 + 45.5625 Combine like terms: 26.25 + 45.5625 = 71.8125 45.5625 + 13.5x + x2 = 71.8125 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 71.8125 Calculate the square root of the right side: 8.474225628 Break this problem into two subproblems by setting (x + 6.75) equal to 8.474225628 and -8.474225628.Subproblem 1
x + 6.75 = 8.474225628 Simplifying x + 6.75 = 8.474225628 Reorder the terms: 6.75 + x = 8.474225628 Solving 6.75 + x = 8.474225628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 8.474225628 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 8.474225628 + -6.75 x = 8.474225628 + -6.75 Combine like terms: 8.474225628 + -6.75 = 1.724225628 x = 1.724225628 Simplifying x = 1.724225628Subproblem 2
x + 6.75 = -8.474225628 Simplifying x + 6.75 = -8.474225628 Reorder the terms: 6.75 + x = -8.474225628 Solving 6.75 + x = -8.474225628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -8.474225628 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -8.474225628 + -6.75 x = -8.474225628 + -6.75 Combine like terms: -8.474225628 + -6.75 = -15.224225628 x = -15.224225628 Simplifying x = -15.224225628Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.724225628, -15.224225628}
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