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Simplifying 0.5x + -0.001x2 = 30 Solving 0.5x + -0.001x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 0.5x + -0.001x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 0.5x + -0.001x2 = 0 Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. 30000 + -500x + x2 = 0 Move the constant term to the right: Add '-30000' to each side of the equation. 30000 + -500x + -30000 + x2 = 0 + -30000 Reorder the terms: 30000 + -30000 + -500x + x2 = 0 + -30000 Combine like terms: 30000 + -30000 = 0 0 + -500x + x2 = 0 + -30000 -500x + x2 = 0 + -30000 Combine like terms: 0 + -30000 = -30000 -500x + x2 = -30000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -30000 + 62500 Reorder the terms: 62500 + -500x + x2 = -30000 + 62500 Combine like terms: -30000 + 62500 = 32500 62500 + -500x + x2 = 32500 Factor a perfect square on the left side: (x + -250)(x + -250) = 32500 Calculate the square root of the right side: 180.277563773 Break this problem into two subproblems by setting (x + -250) equal to 180.277563773 and -180.277563773.Subproblem 1
x + -250 = 180.277563773 Simplifying x + -250 = 180.277563773 Reorder the terms: -250 + x = 180.277563773 Solving -250 + x = 180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 180.277563773 + 250 Combine like terms: -250 + 250 = 0 0 + x = 180.277563773 + 250 x = 180.277563773 + 250 Combine like terms: 180.277563773 + 250 = 430.277563773 x = 430.277563773 Simplifying x = 430.277563773Subproblem 2
x + -250 = -180.277563773 Simplifying x + -250 = -180.277563773 Reorder the terms: -250 + x = -180.277563773 Solving -250 + x = -180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -180.277563773 + 250 Combine like terms: -250 + 250 = 0 0 + x = -180.277563773 + 250 x = -180.277563773 + 250 Combine like terms: -180.277563773 + 250 = 69.722436227 x = 69.722436227 Simplifying x = 69.722436227Solution
The solution to the problem is based on the solutions from the subproblems. x = {430.277563773, 69.722436227}
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