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Simplifying 2x2 = -73x + -20 Reorder the terms: 2x2 = -20 + -73x Solving 2x2 = -20 + -73x Solving for variable 'x'. Reorder the terms: 20 + 73x + 2x2 = -20 + -73x + 20 + 73x Reorder the terms: 20 + 73x + 2x2 = -20 + 20 + -73x + 73x Combine like terms: -20 + 20 = 0 20 + 73x + 2x2 = 0 + -73x + 73x 20 + 73x + 2x2 = -73x + 73x Combine like terms: -73x + 73x = 0 20 + 73x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + 36.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 36.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 36.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 36.5x + x2 = 0 + -10 36.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 36.5x + x2 = -10 The x term is 36.5x. Take half its coefficient (18.25). Square it (333.0625) and add it to both sides. Add '333.0625' to each side of the equation. 36.5x + 333.0625 + x2 = -10 + 333.0625 Reorder the terms: 333.0625 + 36.5x + x2 = -10 + 333.0625 Combine like terms: -10 + 333.0625 = 323.0625 333.0625 + 36.5x + x2 = 323.0625 Factor a perfect square on the left side: (x + 18.25)(x + 18.25) = 323.0625 Calculate the square root of the right side: 17.973939468 Break this problem into two subproblems by setting (x + 18.25) equal to 17.973939468 and -17.973939468.Subproblem 1
x + 18.25 = 17.973939468 Simplifying x + 18.25 = 17.973939468 Reorder the terms: 18.25 + x = 17.973939468 Solving 18.25 + x = 17.973939468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + x = 17.973939468 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + x = 17.973939468 + -18.25 x = 17.973939468 + -18.25 Combine like terms: 17.973939468 + -18.25 = -0.276060532 x = -0.276060532 Simplifying x = -0.276060532Subproblem 2
x + 18.25 = -17.973939468 Simplifying x + 18.25 = -17.973939468 Reorder the terms: 18.25 + x = -17.973939468 Solving 18.25 + x = -17.973939468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + x = -17.973939468 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + x = -17.973939468 + -18.25 x = -17.973939468 + -18.25 Combine like terms: -17.973939468 + -18.25 = -36.223939468 x = -36.223939468 Simplifying x = -36.223939468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.276060532, -36.223939468}
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