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Simplifying 500x + -1x2 = 80 Solving 500x + -1x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 500x + -1x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 500x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -500x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -500x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -500x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -500x + x2 = 0 + -80 -500x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -500x + x2 = -80 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -80 + 62500 Reorder the terms: 62500 + -500x + x2 = -80 + 62500 Combine like terms: -80 + 62500 = 62420 62500 + -500x + x2 = 62420 Factor a perfect square on the left side: (x + -250)(x + -250) = 62420 Calculate the square root of the right side: 249.839948767 Break this problem into two subproblems by setting (x + -250) equal to 249.839948767 and -249.839948767.Subproblem 1
x + -250 = 249.839948767 Simplifying x + -250 = 249.839948767 Reorder the terms: -250 + x = 249.839948767 Solving -250 + x = 249.839948767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 249.839948767 + 250 Combine like terms: -250 + 250 = 0 0 + x = 249.839948767 + 250 x = 249.839948767 + 250 Combine like terms: 249.839948767 + 250 = 499.839948767 x = 499.839948767 Simplifying x = 499.839948767Subproblem 2
x + -250 = -249.839948767 Simplifying x + -250 = -249.839948767 Reorder the terms: -250 + x = -249.839948767 Solving -250 + x = -249.839948767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -249.839948767 + 250 Combine like terms: -250 + 250 = 0 0 + x = -249.839948767 + 250 x = -249.839948767 + 250 Combine like terms: -249.839948767 + 250 = 0.160051233 x = 0.160051233 Simplifying x = 0.160051233Solution
The solution to the problem is based on the solutions from the subproblems. x = {499.839948767, 0.160051233}
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