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Simplifying -1x2 + -80x + 1125 = 0 Reorder the terms: 1125 + -80x + -1x2 = 0 Solving 1125 + -80x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1125 + 80x + x2 = 0 Move the constant term to the right: Add '1125' to each side of the equation. -1125 + 80x + 1125 + x2 = 0 + 1125 Reorder the terms: -1125 + 1125 + 80x + x2 = 0 + 1125 Combine like terms: -1125 + 1125 = 0 0 + 80x + x2 = 0 + 1125 80x + x2 = 0 + 1125 Combine like terms: 0 + 1125 = 1125 80x + x2 = 1125 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 1125 + 1600 Reorder the terms: 1600 + 80x + x2 = 1125 + 1600 Combine like terms: 1125 + 1600 = 2725 1600 + 80x + x2 = 2725 Factor a perfect square on the left side: (x + 40)(x + 40) = 2725 Calculate the square root of the right side: 52.201532545 Break this problem into two subproblems by setting (x + 40) equal to 52.201532545 and -52.201532545.Subproblem 1
x + 40 = 52.201532545 Simplifying x + 40 = 52.201532545 Reorder the terms: 40 + x = 52.201532545 Solving 40 + x = 52.201532545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 52.201532545 + -40 Combine like terms: 40 + -40 = 0 0 + x = 52.201532545 + -40 x = 52.201532545 + -40 Combine like terms: 52.201532545 + -40 = 12.201532545 x = 12.201532545 Simplifying x = 12.201532545Subproblem 2
x + 40 = -52.201532545 Simplifying x + 40 = -52.201532545 Reorder the terms: 40 + x = -52.201532545 Solving 40 + x = -52.201532545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -52.201532545 + -40 Combine like terms: 40 + -40 = 0 0 + x = -52.201532545 + -40 x = -52.201532545 + -40 Combine like terms: -52.201532545 + -40 = -92.201532545 x = -92.201532545 Simplifying x = -92.201532545Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.201532545, -92.201532545}
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