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Simplifying (x + 8) * 2x + x = 180 Reorder the terms: (8 + x) * 2x + x = 180 Reorder the terms for easier multiplication: 2x(8 + x) + x = 180 (8 * 2x + x * 2x) + x = 180 (16x + 2x2) + x = 180 Reorder the terms: 16x + x + 2x2 = 180 Combine like terms: 16x + x = 17x 17x + 2x2 = 180 Solving 17x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 17x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -90 + 8.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 8.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 8.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 8.5x + x2 = 0 + 90 8.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 8.5x + x2 = 90 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 90 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 90 + 18.0625 Combine like terms: 90 + 18.0625 = 108.0625 18.0625 + 8.5x + x2 = 108.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 108.0625 Calculate the square root of the right side: 10.395311443 Break this problem into two subproblems by setting (x + 4.25) equal to 10.395311443 and -10.395311443.Subproblem 1
x + 4.25 = 10.395311443 Simplifying x + 4.25 = 10.395311443 Reorder the terms: 4.25 + x = 10.395311443 Solving 4.25 + x = 10.395311443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 10.395311443 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 10.395311443 + -4.25 x = 10.395311443 + -4.25 Combine like terms: 10.395311443 + -4.25 = 6.145311443 x = 6.145311443 Simplifying x = 6.145311443Subproblem 2
x + 4.25 = -10.395311443 Simplifying x + 4.25 = -10.395311443 Reorder the terms: 4.25 + x = -10.395311443 Solving 4.25 + x = -10.395311443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -10.395311443 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -10.395311443 + -4.25 x = -10.395311443 + -4.25 Combine like terms: -10.395311443 + -4.25 = -14.645311443 x = -14.645311443 Simplifying x = -14.645311443Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.145311443, -14.645311443}
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