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Simplifying 0 = x2 + 82x + -1920 Reorder the terms: 0 = -1920 + 82x + x2 Solving 0 = -1920 + 82x + x2 Solving for variable 'x'. Combine like terms: 0 + 1920 = 1920 1920 + -82x + -1x2 = -1920 + 82x + x2 + 1920 + -82x + -1x2 Reorder the terms: 1920 + -82x + -1x2 = -1920 + 1920 + 82x + -82x + x2 + -1x2 Combine like terms: -1920 + 1920 = 0 1920 + -82x + -1x2 = 0 + 82x + -82x + x2 + -1x2 1920 + -82x + -1x2 = 82x + -82x + x2 + -1x2 Combine like terms: 82x + -82x = 0 1920 + -82x + -1x2 = 0 + x2 + -1x2 1920 + -82x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1920 + -82x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1920 + 82x + x2 = 0 Move the constant term to the right: Add '1920' to each side of the equation. -1920 + 82x + 1920 + x2 = 0 + 1920 Reorder the terms: -1920 + 1920 + 82x + x2 = 0 + 1920 Combine like terms: -1920 + 1920 = 0 0 + 82x + x2 = 0 + 1920 82x + x2 = 0 + 1920 Combine like terms: 0 + 1920 = 1920 82x + x2 = 1920 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 = 1920 + 1681 Reorder the terms: 1681 + 82x + x2 = 1920 + 1681 Combine like terms: 1920 + 1681 = 3601 1681 + 82x + x2 = 3601 Factor a perfect square on the left side: (x + 41)(x + 41) = 3601 Calculate the square root of the right side: 60.008332755 Break this problem into two subproblems by setting (x + 41) equal to 60.008332755 and -60.008332755.Subproblem 1
x + 41 = 60.008332755 Simplifying x + 41 = 60.008332755 Reorder the terms: 41 + x = 60.008332755 Solving 41 + x = 60.008332755 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 = 60.008332755 + -41 Combine like terms: 41 + -41 = 0 0 + x = 60.008332755 + -41 x = 60.008332755 + -41 Combine like terms: 60.008332755 + -41 = 19.008332755 x = 19.008332755 Simplifying x = 19.008332755Subproblem 2
x + 41 = -60.008332755 Simplifying x + 41 = -60.008332755 Reorder the terms: 41 + x = -60.008332755 Solving 41 + x = -60.008332755 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 = -60.008332755 + -41 Combine like terms: 41 + -41 = 0 0 + x = -60.008332755 + -41 x = -60.008332755 + -41 Combine like terms: -60.008332755 + -41 = -101.008332755 x = -101.008332755 Simplifying x = -101.008332755Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.008332755, -101.008332755}
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