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Simplifying x2 + -80x + 1600 = 6375 Reorder the terms: 1600 + -80x + x2 = 6375 Solving 1600 + -80x + x2 = 6375 Solving for variable 'x'. Reorder the terms: 1600 + -6375 + -80x + x2 = 6375 + -6375 Combine like terms: 1600 + -6375 = -4775 -4775 + -80x + x2 = 6375 + -6375 Combine like terms: 6375 + -6375 = 0 -4775 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4775' to each side of the equation. -4775 + -80x + 4775 + x2 = 0 + 4775 Reorder the terms: -4775 + 4775 + -80x + x2 = 0 + 4775 Combine like terms: -4775 + 4775 = 0 0 + -80x + x2 = 0 + 4775 -80x + x2 = 0 + 4775 Combine like terms: 0 + 4775 = 4775 -80x + x2 = 4775 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 = 4775 + 1600 Reorder the terms: 1600 + -80x + x2 = 4775 + 1600 Combine like terms: 4775 + 1600 = 6375 1600 + -80x + x2 = 6375 Factor a perfect square on the left side: (x + -40)(x + -40) = 6375 Calculate the square root of the right side: 79.843597113 Break this problem into two subproblems by setting (x + -40) equal to 79.843597113 and -79.843597113.Subproblem 1
x + -40 = 79.843597113 Simplifying x + -40 = 79.843597113 Reorder the terms: -40 + x = 79.843597113 Solving -40 + x = 79.843597113 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 = 79.843597113 + 40 Combine like terms: -40 + 40 = 0 0 + x = 79.843597113 + 40 x = 79.843597113 + 40 Combine like terms: 79.843597113 + 40 = 119.843597113 x = 119.843597113 Simplifying x = 119.843597113Subproblem 2
x + -40 = -79.843597113 Simplifying x + -40 = -79.843597113 Reorder the terms: -40 + x = -79.843597113 Solving -40 + x = -79.843597113 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 = -79.843597113 + 40 Combine like terms: -40 + 40 = 0 0 + x = -79.843597113 + 40 x = -79.843597113 + 40 Combine like terms: -79.843597113 + 40 = -39.843597113 x = -39.843597113 Simplifying x = -39.843597113Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.843597113, -39.843597113}
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