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Simplifying x2 + 82x + -525 = 0 Reorder the terms: -525 + 82x + x2 = 0 Solving -525 + 82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '525' to each side of the equation. -525 + 82x + 525 + x2 = 0 + 525 Reorder the terms: -525 + 525 + 82x + x2 = 0 + 525 Combine like terms: -525 + 525 = 0 0 + 82x + x2 = 0 + 525 82x + x2 = 0 + 525 Combine like terms: 0 + 525 = 525 82x + x2 = 525 The x term is 82x. Take half its coefficient (41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. 82x + 1681 + x2 = 525 + 1681 Reorder the terms: 1681 + 82x + x2 = 525 + 1681 Combine like terms: 525 + 1681 = 2206 1681 + 82x + x2 = 2206 Factor a perfect square on the left side: (x + 41)(x + 41) = 2206 Calculate the square root of the right side: 46.968074263 Break this problem into two subproblems by setting (x + 41) equal to 46.968074263 and -46.968074263.Subproblem 1
x + 41 = 46.968074263 Simplifying x + 41 = 46.968074263 Reorder the terms: 41 + x = 46.968074263 Solving 41 + x = 46.968074263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + x = 46.968074263 + -41 Combine like terms: 41 + -41 = 0 0 + x = 46.968074263 + -41 x = 46.968074263 + -41 Combine like terms: 46.968074263 + -41 = 5.968074263 x = 5.968074263 Simplifying x = 5.968074263Subproblem 2
x + 41 = -46.968074263 Simplifying x + 41 = -46.968074263 Reorder the terms: 41 + x = -46.968074263 Solving 41 + x = -46.968074263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + x = -46.968074263 + -41 Combine like terms: 41 + -41 = 0 0 + x = -46.968074263 + -41 x = -46.968074263 + -41 Combine like terms: -46.968074263 + -41 = -87.968074263 x = -87.968074263 Simplifying x = -87.968074263Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.968074263, -87.968074263}
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