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Simplifying -0.2x2 + 90x + -2000 = 0 Reorder the terms: -2000 + 90x + -0.2x2 = 0 Solving -2000 + 90x + -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'. 10000 + -450x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + -450x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + -450x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + -450x + x2 = 0 + -10000 -450x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 -450x + x2 = -10000 The x term is -450x. Take half its coefficient (-225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. -450x + 50625 + x2 = -10000 + 50625 Reorder the terms: 50625 + -450x + x2 = -10000 + 50625 Combine like terms: -10000 + 50625 = 40625 50625 + -450x + x2 = 40625 Factor a perfect square on the left side: (x + -225)(x + -225) = 40625 Calculate the square root of the right side: 201.556443707 Break this problem into two subproblems by setting (x + -225) equal to 201.556443707 and -201.556443707.Subproblem 1
x + -225 = 201.556443707 Simplifying x + -225 = 201.556443707 Reorder the terms: -225 + x = 201.556443707 Solving -225 + x = 201.556443707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = 201.556443707 + 225 Combine like terms: -225 + 225 = 0 0 + x = 201.556443707 + 225 x = 201.556443707 + 225 Combine like terms: 201.556443707 + 225 = 426.556443707 x = 426.556443707 Simplifying x = 426.556443707Subproblem 2
x + -225 = -201.556443707 Simplifying x + -225 = -201.556443707 Reorder the terms: -225 + x = -201.556443707 Solving -225 + x = -201.556443707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = -201.556443707 + 225 Combine like terms: -225 + 225 = 0 0 + x = -201.556443707 + 225 x = -201.556443707 + 225 Combine like terms: -201.556443707 + 225 = 23.443556293 x = 23.443556293 Simplifying x = 23.443556293Solution
The solution to the problem is based on the solutions from the subproblems. x = {426.556443707, 23.443556293}
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