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Simplifying (2x + 1)(x + 15) = 180 Reorder the terms: (1 + 2x)(x + 15) = 180 Reorder the terms: (1 + 2x)(15 + x) = 180 Multiply (1 + 2x) * (15 + x) (1(15 + x) + 2x * (15 + x)) = 180 ((15 * 1 + x * 1) + 2x * (15 + x)) = 180 ((15 + 1x) + 2x * (15 + x)) = 180 (15 + 1x + (15 * 2x + x * 2x)) = 180 (15 + 1x + (30x + 2x2)) = 180 Combine like terms: 1x + 30x = 31x (15 + 31x + 2x2) = 180 Solving 15 + 31x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 15 + -180 + 31x + 2x2 = 180 + -180 Combine like terms: 15 + -180 = -165 -165 + 31x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -165 + 31x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -82.5 + 15.5x + x2 = 0 Move the constant term to the right: Add '82.5' to each side of the equation. -82.5 + 15.5x + 82.5 + x2 = 0 + 82.5 Reorder the terms: -82.5 + 82.5 + 15.5x + x2 = 0 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + 15.5x + x2 = 0 + 82.5 15.5x + x2 = 0 + 82.5 Combine like terms: 0 + 82.5 = 82.5 15.5x + x2 = 82.5 The x term is 15.5x. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5x + 60.0625 + x2 = 82.5 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = 82.5 + 60.0625 Combine like terms: 82.5 + 60.0625 = 142.5625 60.0625 + 15.5x + x2 = 142.5625 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 142.5625 Calculate the square root of the right side: 11.939953936 Break this problem into two subproblems by setting (x + 7.75) equal to 11.939953936 and -11.939953936.Subproblem 1
x + 7.75 = 11.939953936 Simplifying x + 7.75 = 11.939953936 Reorder the terms: 7.75 + x = 11.939953936 Solving 7.75 + x = 11.939953936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 11.939953936 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 11.939953936 + -7.75 x = 11.939953936 + -7.75 Combine like terms: 11.939953936 + -7.75 = 4.189953936 x = 4.189953936 Simplifying x = 4.189953936Subproblem 2
x + 7.75 = -11.939953936 Simplifying x + 7.75 = -11.939953936 Reorder the terms: 7.75 + x = -11.939953936 Solving 7.75 + x = -11.939953936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -11.939953936 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -11.939953936 + -7.75 x = -11.939953936 + -7.75 Combine like terms: -11.939953936 + -7.75 = -19.689953936 x = -19.689953936 Simplifying x = -19.689953936Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.189953936, -19.689953936}
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