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Simplifying x2 + -82x + 408 = 0 Reorder the terms: 408 + -82x + x2 = 0 Solving 408 + -82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-408' to each side of the equation. 408 + -82x + -408 + x2 = 0 + -408 Reorder the terms: 408 + -408 + -82x + x2 = 0 + -408 Combine like terms: 408 + -408 = 0 0 + -82x + x2 = 0 + -408 -82x + x2 = 0 + -408 Combine like terms: 0 + -408 = -408 -82x + x2 = -408 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 = -408 + 1681 Reorder the terms: 1681 + -82x + x2 = -408 + 1681 Combine like terms: -408 + 1681 = 1273 1681 + -82x + x2 = 1273 Factor a perfect square on the left side: (x + -41)(x + -41) = 1273 Calculate the square root of the right side: 35.67912555 Break this problem into two subproblems by setting (x + -41) equal to 35.67912555 and -35.67912555.Subproblem 1
x + -41 = 35.67912555 Simplifying x + -41 = 35.67912555 Reorder the terms: -41 + x = 35.67912555 Solving -41 + x = 35.67912555 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 = 35.67912555 + 41 Combine like terms: -41 + 41 = 0 0 + x = 35.67912555 + 41 x = 35.67912555 + 41 Combine like terms: 35.67912555 + 41 = 76.67912555 x = 76.67912555 Simplifying x = 76.67912555Subproblem 2
x + -41 = -35.67912555 Simplifying x + -41 = -35.67912555 Reorder the terms: -41 + x = -35.67912555 Solving -41 + x = -35.67912555 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 = -35.67912555 + 41 Combine like terms: -41 + 41 = 0 0 + x = -35.67912555 + 41 x = -35.67912555 + 41 Combine like terms: -35.67912555 + 41 = 5.32087445 x = 5.32087445 Simplifying x = 5.32087445Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.67912555, 5.32087445}
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