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Simplifying x2 + -82x + 8 = 0 Reorder the terms: 8 + -82x + x2 = 0 Solving 8 + -82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -82x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -82x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -82x + x2 = 0 + -8 -82x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -82x + x2 = -8 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 = -8 + 1681 Reorder the terms: 1681 + -82x + x2 = -8 + 1681 Combine like terms: -8 + 1681 = 1673 1681 + -82x + x2 = 1673 Factor a perfect square on the left side: (x + -41)(x + -41) = 1673 Calculate the square root of the right side: 40.902322672 Break this problem into two subproblems by setting (x + -41) equal to 40.902322672 and -40.902322672.Subproblem 1
x + -41 = 40.902322672 Simplifying x + -41 = 40.902322672 Reorder the terms: -41 + x = 40.902322672 Solving -41 + x = 40.902322672 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 = 40.902322672 + 41 Combine like terms: -41 + 41 = 0 0 + x = 40.902322672 + 41 x = 40.902322672 + 41 Combine like terms: 40.902322672 + 41 = 81.902322672 x = 81.902322672 Simplifying x = 81.902322672Subproblem 2
x + -41 = -40.902322672 Simplifying x + -41 = -40.902322672 Reorder the terms: -41 + x = -40.902322672 Solving -41 + x = -40.902322672 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 = -40.902322672 + 41 Combine like terms: -41 + 41 = 0 0 + x = -40.902322672 + 41 x = -40.902322672 + 41 Combine like terms: -40.902322672 + 41 = 0.097677328 x = 0.097677328 Simplifying x = 0.097677328Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.902322672, 0.097677328}
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