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Simplifying 0.5x(x + 6) = 11664 Reorder the terms: 0.5x(6 + x) = 11664 (6 * 0.5x + x * 0.5x) = 11664 (3x + 0.5x2) = 11664 Solving 3x + 0.5x2 = 11664 Solving for variable 'x'. Reorder the terms: -11664 + 3x + 0.5x2 = 11664 + -11664 Combine like terms: 11664 + -11664 = 0 -11664 + 3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -23328 + 6x + x2 = 0 Move the constant term to the right: Add '23328' to each side of the equation. -23328 + 6x + 23328 + x2 = 0 + 23328 Reorder the terms: -23328 + 23328 + 6x + x2 = 0 + 23328 Combine like terms: -23328 + 23328 = 0 0 + 6x + x2 = 0 + 23328 6x + x2 = 0 + 23328 Combine like terms: 0 + 23328 = 23328 6x + x2 = 23328 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 23328 + 9 Reorder the terms: 9 + 6x + x2 = 23328 + 9 Combine like terms: 23328 + 9 = 23337 9 + 6x + x2 = 23337 Factor a perfect square on the left side: (x + 3)(x + 3) = 23337 Calculate the square root of the right side: 152.764524678 Break this problem into two subproblems by setting (x + 3) equal to 152.764524678 and -152.764524678.Subproblem 1
x + 3 = 152.764524678 Simplifying x + 3 = 152.764524678 Reorder the terms: 3 + x = 152.764524678 Solving 3 + x = 152.764524678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 152.764524678 + -3 Combine like terms: 3 + -3 = 0 0 + x = 152.764524678 + -3 x = 152.764524678 + -3 Combine like terms: 152.764524678 + -3 = 149.764524678 x = 149.764524678 Simplifying x = 149.764524678Subproblem 2
x + 3 = -152.764524678 Simplifying x + 3 = -152.764524678 Reorder the terms: 3 + x = -152.764524678 Solving 3 + x = -152.764524678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -152.764524678 + -3 Combine like terms: 3 + -3 = 0 0 + x = -152.764524678 + -3 x = -152.764524678 + -3 Combine like terms: -152.764524678 + -3 = -155.764524678 x = -155.764524678 Simplifying x = -155.764524678Solution
The solution to the problem is based on the solutions from the subproblems. x = {149.764524678, -155.764524678}
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