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Simplifying 2x2 + 17x = 179 Reorder the terms: 17x + 2x2 = 179 Solving 17x + 2x2 = 179 Solving for variable 'x'. Reorder the terms: -179 + 17x + 2x2 = 179 + -179 Combine like terms: 179 + -179 = 0 -179 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -89.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '89.5' to each side of the equation. -89.5 + 8.5x + 89.5 + x2 = 0 + 89.5 Reorder the terms: -89.5 + 89.5 + 8.5x + x2 = 0 + 89.5 Combine like terms: -89.5 + 89.5 = 0.0 0.0 + 8.5x + x2 = 0 + 89.5 8.5x + x2 = 0 + 89.5 Combine like terms: 0 + 89.5 = 89.5 8.5x + x2 = 89.5 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 = 89.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 89.5 + 18.0625 Combine like terms: 89.5 + 18.0625 = 107.5625 18.0625 + 8.5x + x2 = 107.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 107.5625 Calculate the square root of the right side: 10.371234256 Break this problem into two subproblems by setting (x + 4.25) equal to 10.371234256 and -10.371234256.Subproblem 1
x + 4.25 = 10.371234256 Simplifying x + 4.25 = 10.371234256 Reorder the terms: 4.25 + x = 10.371234256 Solving 4.25 + x = 10.371234256 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 = 10.371234256 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 10.371234256 + -4.25 x = 10.371234256 + -4.25 Combine like terms: 10.371234256 + -4.25 = 6.121234256 x = 6.121234256 Simplifying x = 6.121234256Subproblem 2
x + 4.25 = -10.371234256 Simplifying x + 4.25 = -10.371234256 Reorder the terms: 4.25 + x = -10.371234256 Solving 4.25 + x = -10.371234256 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 = -10.371234256 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -10.371234256 + -4.25 x = -10.371234256 + -4.25 Combine like terms: -10.371234256 + -4.25 = -14.621234256 x = -14.621234256 Simplifying x = -14.621234256Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.121234256, -14.621234256}
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