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Simplifying -2.5x2 + 2825x + -500000 = 0 Reorder the terms: -500000 + 2825x + -2.5x2 = 0 Solving -500000 + 2825x + -2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. 200000 + -1130x + x2 = 0 Move the constant term to the right: Add '-200000' to each side of the equation. 200000 + -1130x + -200000 + x2 = 0 + -200000 Reorder the terms: 200000 + -200000 + -1130x + x2 = 0 + -200000 Combine like terms: 200000 + -200000 = 0 0 + -1130x + x2 = 0 + -200000 -1130x + x2 = 0 + -200000 Combine like terms: 0 + -200000 = -200000 -1130x + x2 = -200000 The x term is -1130x. Take half its coefficient (-565). Square it (319225) and add it to both sides. Add '319225' to each side of the equation. -1130x + 319225 + x2 = -200000 + 319225 Reorder the terms: 319225 + -1130x + x2 = -200000 + 319225 Combine like terms: -200000 + 319225 = 119225 319225 + -1130x + x2 = 119225 Factor a perfect square on the left side: (x + -565)(x + -565) = 119225 Calculate the square root of the right side: 345.289733412 Break this problem into two subproblems by setting (x + -565) equal to 345.289733412 and -345.289733412.Subproblem 1
x + -565 = 345.289733412 Simplifying x + -565 = 345.289733412 Reorder the terms: -565 + x = 345.289733412 Solving -565 + x = 345.289733412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '565' to each side of the equation. -565 + 565 + x = 345.289733412 + 565 Combine like terms: -565 + 565 = 0 0 + x = 345.289733412 + 565 x = 345.289733412 + 565 Combine like terms: 345.289733412 + 565 = 910.289733412 x = 910.289733412 Simplifying x = 910.289733412Subproblem 2
x + -565 = -345.289733412 Simplifying x + -565 = -345.289733412 Reorder the terms: -565 + x = -345.289733412 Solving -565 + x = -345.289733412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '565' to each side of the equation. -565 + 565 + x = -345.289733412 + 565 Combine like terms: -565 + 565 = 0 0 + x = -345.289733412 + 565 x = -345.289733412 + 565 Combine like terms: -345.289733412 + 565 = 219.710266588 x = 219.710266588 Simplifying x = 219.710266588Solution
The solution to the problem is based on the solutions from the subproblems. x = {910.289733412, 219.710266588}
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