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Simplifying x2 + 82x + -832 = 0 Reorder the terms: -832 + 82x + x2 = 0 Solving -832 + 82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '832' to each side of the equation. -832 + 82x + 832 + x2 = 0 + 832 Reorder the terms: -832 + 832 + 82x + x2 = 0 + 832 Combine like terms: -832 + 832 = 0 0 + 82x + x2 = 0 + 832 82x + x2 = 0 + 832 Combine like terms: 0 + 832 = 832 82x + x2 = 832 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 = 832 + 1681 Reorder the terms: 1681 + 82x + x2 = 832 + 1681 Combine like terms: 832 + 1681 = 2513 1681 + 82x + x2 = 2513 Factor a perfect square on the left side: (x + 41)(x + 41) = 2513 Calculate the square root of the right side: 50.129831438 Break this problem into two subproblems by setting (x + 41) equal to 50.129831438 and -50.129831438.Subproblem 1
x + 41 = 50.129831438 Simplifying x + 41 = 50.129831438 Reorder the terms: 41 + x = 50.129831438 Solving 41 + x = 50.129831438 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 = 50.129831438 + -41 Combine like terms: 41 + -41 = 0 0 + x = 50.129831438 + -41 x = 50.129831438 + -41 Combine like terms: 50.129831438 + -41 = 9.129831438 x = 9.129831438 Simplifying x = 9.129831438Subproblem 2
x + 41 = -50.129831438 Simplifying x + 41 = -50.129831438 Reorder the terms: 41 + x = -50.129831438 Solving 41 + x = -50.129831438 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 = -50.129831438 + -41 Combine like terms: 41 + -41 = 0 0 + x = -50.129831438 + -41 x = -50.129831438 + -41 Combine like terms: -50.129831438 + -41 = -91.129831438 x = -91.129831438 Simplifying x = -91.129831438Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.129831438, -91.129831438}
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