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Simplifying -2.5x2 + 2825x + -115812.5 = 500000 Reorder the terms: -115812.5 + 2825x + -2.5x2 = 500000 Solving -115812.5 + 2825x + -2.5x2 = 500000 Solving for variable 'x'. Reorder the terms: -115812.5 + -500000 + 2825x + -2.5x2 = 500000 + -500000 Combine like terms: -115812.5 + -500000 = -615812.5 -615812.5 + 2825x + -2.5x2 = 500000 + -500000 Combine like terms: 500000 + -500000 = 0 -615812.5 + 2825x + -2.5x2 = 0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. 246325 + -1130x + x2 = 0 Move the constant term to the right: Add '-246325' to each side of the equation. 246325 + -1130x + -246325 + x2 = 0 + -246325 Reorder the terms: 246325 + -246325 + -1130x + x2 = 0 + -246325 Combine like terms: 246325 + -246325 = 0 0 + -1130x + x2 = 0 + -246325 -1130x + x2 = 0 + -246325 Combine like terms: 0 + -246325 = -246325 -1130x + x2 = -246325 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 = -246325 + 319225 Reorder the terms: 319225 + -1130x + x2 = -246325 + 319225 Combine like terms: -246325 + 319225 = 72900 319225 + -1130x + x2 = 72900 Factor a perfect square on the left side: (x + -565)(x + -565) = 72900 Calculate the square root of the right side: 270 Break this problem into two subproblems by setting (x + -565) equal to 270 and -270.Subproblem 1
x + -565 = 270 Simplifying x + -565 = 270 Reorder the terms: -565 + x = 270 Solving -565 + x = 270 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 = 270 + 565 Combine like terms: -565 + 565 = 0 0 + x = 270 + 565 x = 270 + 565 Combine like terms: 270 + 565 = 835 x = 835 Simplifying x = 835Subproblem 2
x + -565 = -270 Simplifying x + -565 = -270 Reorder the terms: -565 + x = -270 Solving -565 + x = -270 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 = -270 + 565 Combine like terms: -565 + 565 = 0 0 + x = -270 + 565 x = -270 + 565 Combine like terms: -270 + 565 = 295 x = 295 Simplifying x = 295Solution
The solution to the problem is based on the solutions from the subproblems. x = {835, 295}
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