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Simplifying -0.02x2 + 200x + -80000 = 0 Reorder the terms: -80000 + 200x + -0.02x2 = 0 Solving -80000 + 200x + -0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 4000000 + -10000x + x2 = 0 Move the constant term to the right: Add '-4000000' to each side of the equation. 4000000 + -10000x + -4000000 + x2 = 0 + -4000000 Reorder the terms: 4000000 + -4000000 + -10000x + x2 = 0 + -4000000 Combine like terms: 4000000 + -4000000 = 0 0 + -10000x + x2 = 0 + -4000000 -10000x + x2 = 0 + -4000000 Combine like terms: 0 + -4000000 = -4000000 -10000x + x2 = -4000000 The x term is -10000x. Take half its coefficient (-5000). Square it (25000000) and add it to both sides. Add '25000000' to each side of the equation. -10000x + 25000000 + x2 = -4000000 + 25000000 Reorder the terms: 25000000 + -10000x + x2 = -4000000 + 25000000 Combine like terms: -4000000 + 25000000 = 21000000 25000000 + -10000x + x2 = 21000000 Factor a perfect square on the left side: (x + -5000)(x + -5000) = 21000000 Calculate the square root of the right side: 4582.575694956 Break this problem into two subproblems by setting (x + -5000) equal to 4582.575694956 and -4582.575694956.Subproblem 1
x + -5000 = 4582.575694956 Simplifying x + -5000 = 4582.575694956 Reorder the terms: -5000 + x = 4582.575694956 Solving -5000 + x = 4582.575694956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = 4582.575694956 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = 4582.575694956 + 5000 x = 4582.575694956 + 5000 Combine like terms: 4582.575694956 + 5000 = 9582.575694956 x = 9582.575694956 Simplifying x = 9582.575694956Subproblem 2
x + -5000 = -4582.575694956 Simplifying x + -5000 = -4582.575694956 Reorder the terms: -5000 + x = -4582.575694956 Solving -5000 + x = -4582.575694956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = -4582.575694956 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = -4582.575694956 + 5000 x = -4582.575694956 + 5000 Combine like terms: -4582.575694956 + 5000 = 417.424305044 x = 417.424305044 Simplifying x = 417.424305044Solution
The solution to the problem is based on the solutions from the subproblems. x = {9582.575694956, 417.424305044}
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