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Simplifying (2x + 5)(2x + 1) = 360 Reorder the terms: (5 + 2x)(2x + 1) = 360 Reorder the terms: (5 + 2x)(1 + 2x) = 360 Multiply (5 + 2x) * (1 + 2x) (5(1 + 2x) + 2x * (1 + 2x)) = 360 ((1 * 5 + 2x * 5) + 2x * (1 + 2x)) = 360 ((5 + 10x) + 2x * (1 + 2x)) = 360 (5 + 10x + (1 * 2x + 2x * 2x)) = 360 (5 + 10x + (2x + 4x2)) = 360 Combine like terms: 10x + 2x = 12x (5 + 12x + 4x2) = 360 Solving 5 + 12x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: 5 + -360 + 12x + 4x2 = 360 + -360 Combine like terms: 5 + -360 = -355 -355 + 12x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -355 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -88.75 + 3x + x2 = 0 Move the constant term to the right: Add '88.75' to each side of the equation. -88.75 + 3x + 88.75 + x2 = 0 + 88.75 Reorder the terms: -88.75 + 88.75 + 3x + x2 = 0 + 88.75 Combine like terms: -88.75 + 88.75 = 0.00 0.00 + 3x + x2 = 0 + 88.75 3x + x2 = 0 + 88.75 Combine like terms: 0 + 88.75 = 88.75 3x + x2 = 88.75 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 = 88.75 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 88.75 + 2.25 Combine like terms: 88.75 + 2.25 = 91 2.25 + 3x + x2 = 91 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + 1.5) equal to 9.539392014 and -9.539392014.Subproblem 1
x + 1.5 = 9.539392014 Simplifying x + 1.5 = 9.539392014 Reorder the terms: 1.5 + x = 9.539392014 Solving 1.5 + x = 9.539392014 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 = 9.539392014 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.539392014 + -1.5 x = 9.539392014 + -1.5 Combine like terms: 9.539392014 + -1.5 = 8.039392014 x = 8.039392014 Simplifying x = 8.039392014Subproblem 2
x + 1.5 = -9.539392014 Simplifying x + 1.5 = -9.539392014 Reorder the terms: 1.5 + x = -9.539392014 Solving 1.5 + x = -9.539392014 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 = -9.539392014 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.539392014 + -1.5 x = -9.539392014 + -1.5 Combine like terms: -9.539392014 + -1.5 = -11.039392014 x = -11.039392014 Simplifying x = -11.039392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.039392014, -11.039392014}
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