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Simplifying (2x + 3)(x) = 360 Reorder the terms: (3 + 2x)(x) = 360 Reorder the terms for easier multiplication: x(3 + 2x) = 360 (3 * x + 2x * x) = 360 (3x + 2x2) = 360 Solving 3x + 2x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 3x + 2x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -180 + 1.5x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 1.5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 1.5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 1.5x + x2 = 0 + 180 1.5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 1.5x + x2 = 180 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 180 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 180 + 0.5625 Combine like terms: 180 + 0.5625 = 180.5625 0.5625 + 1.5x + x2 = 180.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 180.5625 Calculate the square root of the right side: 13.43735465 Break this problem into two subproblems by setting (x + 0.75) equal to 13.43735465 and -13.43735465.Subproblem 1
x + 0.75 = 13.43735465 Simplifying x + 0.75 = 13.43735465 Reorder the terms: 0.75 + x = 13.43735465 Solving 0.75 + x = 13.43735465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 13.43735465 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 13.43735465 + -0.75 x = 13.43735465 + -0.75 Combine like terms: 13.43735465 + -0.75 = 12.68735465 x = 12.68735465 Simplifying x = 12.68735465Subproblem 2
x + 0.75 = -13.43735465 Simplifying x + 0.75 = -13.43735465 Reorder the terms: 0.75 + x = -13.43735465 Solving 0.75 + x = -13.43735465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -13.43735465 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -13.43735465 + -0.75 x = -13.43735465 + -0.75 Combine like terms: -13.43735465 + -0.75 = -14.18735465 x = -14.18735465 Simplifying x = -14.18735465Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.68735465, -14.18735465}
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