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Simplifying x2 + 80x + -820 = 0 Reorder the terms: -820 + 80x + x2 = 0 Solving -820 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '820' to each side of the equation. -820 + 80x + 820 + x2 = 0 + 820 Reorder the terms: -820 + 820 + 80x + x2 = 0 + 820 Combine like terms: -820 + 820 = 0 0 + 80x + x2 = 0 + 820 80x + x2 = 0 + 820 Combine like terms: 0 + 820 = 820 80x + x2 = 820 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 820 + 1600 Reorder the terms: 1600 + 80x + x2 = 820 + 1600 Combine like terms: 820 + 1600 = 2420 1600 + 80x + x2 = 2420 Factor a perfect square on the left side: (x + 40)(x + 40) = 2420 Calculate the square root of the right side: 49.193495505 Break this problem into two subproblems by setting (x + 40) equal to 49.193495505 and -49.193495505.Subproblem 1
x + 40 = 49.193495505 Simplifying x + 40 = 49.193495505 Reorder the terms: 40 + x = 49.193495505 Solving 40 + x = 49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 49.193495505 + -40 Combine like terms: 40 + -40 = 0 0 + x = 49.193495505 + -40 x = 49.193495505 + -40 Combine like terms: 49.193495505 + -40 = 9.193495505 x = 9.193495505 Simplifying x = 9.193495505Subproblem 2
x + 40 = -49.193495505 Simplifying x + 40 = -49.193495505 Reorder the terms: 40 + x = -49.193495505 Solving 40 + x = -49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -49.193495505 + -40 Combine like terms: 40 + -40 = 0 0 + x = -49.193495505 + -40 x = -49.193495505 + -40 Combine like terms: -49.193495505 + -40 = -89.193495505 x = -89.193495505 Simplifying x = -89.193495505Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.193495505, -89.193495505}
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