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Simplifying x2 + 82x + -180 = 0 Reorder the terms: -180 + 82x + x2 = 0 Solving -180 + 82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 82x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 82x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 82x + x2 = 0 + 180 82x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 82x + x2 = 180 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 = 180 + 1681 Reorder the terms: 1681 + 82x + x2 = 180 + 1681 Combine like terms: 180 + 1681 = 1861 1681 + 82x + x2 = 1861 Factor a perfect square on the left side: (x + 41)(x + 41) = 1861 Calculate the square root of the right side: 43.13930922 Break this problem into two subproblems by setting (x + 41) equal to 43.13930922 and -43.13930922.Subproblem 1
x + 41 = 43.13930922 Simplifying x + 41 = 43.13930922 Reorder the terms: 41 + x = 43.13930922 Solving 41 + x = 43.13930922 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 = 43.13930922 + -41 Combine like terms: 41 + -41 = 0 0 + x = 43.13930922 + -41 x = 43.13930922 + -41 Combine like terms: 43.13930922 + -41 = 2.13930922 x = 2.13930922 Simplifying x = 2.13930922Subproblem 2
x + 41 = -43.13930922 Simplifying x + 41 = -43.13930922 Reorder the terms: 41 + x = -43.13930922 Solving 41 + x = -43.13930922 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 = -43.13930922 + -41 Combine like terms: 41 + -41 = 0 0 + x = -43.13930922 + -41 x = -43.13930922 + -41 Combine like terms: -43.13930922 + -41 = -84.13930922 x = -84.13930922 Simplifying x = -84.13930922Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.13930922, -84.13930922}
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