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Simplifying -2.5x2 + 2825x + -115812.5 = 0 Reorder the terms: -115812.5 + 2825x + -2.5x2 = 0 Solving -115812.5 + 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'. 46325 + -1130x + x2 = 0 Move the constant term to the right: Add '-46325' to each side of the equation. 46325 + -1130x + -46325 + x2 = 0 + -46325 Reorder the terms: 46325 + -46325 + -1130x + x2 = 0 + -46325 Combine like terms: 46325 + -46325 = 0 0 + -1130x + x2 = 0 + -46325 -1130x + x2 = 0 + -46325 Combine like terms: 0 + -46325 = -46325 -1130x + x2 = -46325 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 = -46325 + 319225 Reorder the terms: 319225 + -1130x + x2 = -46325 + 319225 Combine like terms: -46325 + 319225 = 272900 319225 + -1130x + x2 = 272900 Factor a perfect square on the left side: (x + -565)(x + -565) = 272900 Calculate the square root of the right side: 522.398315464 Break this problem into two subproblems by setting (x + -565) equal to 522.398315464 and -522.398315464.Subproblem 1
x + -565 = 522.398315464 Simplifying x + -565 = 522.398315464 Reorder the terms: -565 + x = 522.398315464 Solving -565 + x = 522.398315464 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 = 522.398315464 + 565 Combine like terms: -565 + 565 = 0 0 + x = 522.398315464 + 565 x = 522.398315464 + 565 Combine like terms: 522.398315464 + 565 = 1087.398315464 x = 1087.398315464 Simplifying x = 1087.398315464Subproblem 2
x + -565 = -522.398315464 Simplifying x + -565 = -522.398315464 Reorder the terms: -565 + x = -522.398315464 Solving -565 + x = -522.398315464 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 = -522.398315464 + 565 Combine like terms: -565 + 565 = 0 0 + x = -522.398315464 + 565 x = -522.398315464 + 565 Combine like terms: -522.398315464 + 565 = 42.601684536 x = 42.601684536 Simplifying x = 42.601684536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1087.398315464, 42.601684536}
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