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Simplifying -0.2x2 + 160x + -9800 = 0 Reorder the terms: -9800 + 160x + -0.2x2 = 0 Solving -9800 + 160x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 49000 + -800x + x2 = 0 Move the constant term to the right: Add '-49000' to each side of the equation. 49000 + -800x + -49000 + x2 = 0 + -49000 Reorder the terms: 49000 + -49000 + -800x + x2 = 0 + -49000 Combine like terms: 49000 + -49000 = 0 0 + -800x + x2 = 0 + -49000 -800x + x2 = 0 + -49000 Combine like terms: 0 + -49000 = -49000 -800x + x2 = -49000 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -49000 + 160000 Reorder the terms: 160000 + -800x + x2 = -49000 + 160000 Combine like terms: -49000 + 160000 = 111000 160000 + -800x + x2 = 111000 Factor a perfect square on the left side: (x + -400)(x + -400) = 111000 Calculate the square root of the right side: 333.166624979 Break this problem into two subproblems by setting (x + -400) equal to 333.166624979 and -333.166624979.Subproblem 1
x + -400 = 333.166624979 Simplifying x + -400 = 333.166624979 Reorder the terms: -400 + x = 333.166624979 Solving -400 + x = 333.166624979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 333.166624979 + 400 Combine like terms: -400 + 400 = 0 0 + x = 333.166624979 + 400 x = 333.166624979 + 400 Combine like terms: 333.166624979 + 400 = 733.166624979 x = 733.166624979 Simplifying x = 733.166624979Subproblem 2
x + -400 = -333.166624979 Simplifying x + -400 = -333.166624979 Reorder the terms: -400 + x = -333.166624979 Solving -400 + x = -333.166624979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -333.166624979 + 400 Combine like terms: -400 + 400 = 0 0 + x = -333.166624979 + 400 x = -333.166624979 + 400 Combine like terms: -333.166624979 + 400 = 66.833375021 x = 66.833375021 Simplifying x = 66.833375021Solution
The solution to the problem is based on the solutions from the subproblems. x = {733.166624979, 66.833375021}
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