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Simplifying x2 + -80x + 250 = 0 Reorder the terms: 250 + -80x + x2 = 0 Solving 250 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -80x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -80x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -80x + x2 = 0 + -250 -80x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -80x + x2 = -250 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 = -250 + 1600 Reorder the terms: 1600 + -80x + x2 = -250 + 1600 Combine like terms: -250 + 1600 = 1350 1600 + -80x + x2 = 1350 Factor a perfect square on the left side: (x + -40)(x + -40) = 1350 Calculate the square root of the right side: 36.742346142 Break this problem into two subproblems by setting (x + -40) equal to 36.742346142 and -36.742346142.Subproblem 1
x + -40 = 36.742346142 Simplifying x + -40 = 36.742346142 Reorder the terms: -40 + x = 36.742346142 Solving -40 + x = 36.742346142 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 = 36.742346142 + 40 Combine like terms: -40 + 40 = 0 0 + x = 36.742346142 + 40 x = 36.742346142 + 40 Combine like terms: 36.742346142 + 40 = 76.742346142 x = 76.742346142 Simplifying x = 76.742346142Subproblem 2
x + -40 = -36.742346142 Simplifying x + -40 = -36.742346142 Reorder the terms: -40 + x = -36.742346142 Solving -40 + x = -36.742346142 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 = -36.742346142 + 40 Combine like terms: -40 + 40 = 0 0 + x = -36.742346142 + 40 x = -36.742346142 + 40 Combine like terms: -36.742346142 + 40 = 3.257653858 x = 3.257653858 Simplifying x = 3.257653858Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.742346142, 3.257653858}
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