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Simplifying (x) = 200 + -10x + 0.01x2 x = 200 + -10x + 0.01x2 Solving x = 200 + -10x + 0.01x2 Solving for variable 'x'. Reorder the terms: -200 + x + 10x + -0.01x2 = 200 + -10x + 0.01x2 + -200 + 10x + -0.01x2 Combine like terms: x + 10x = 11x -200 + 11x + -0.01x2 = 200 + -10x + 0.01x2 + -200 + 10x + -0.01x2 Reorder the terms: -200 + 11x + -0.01x2 = 200 + -200 + -10x + 10x + 0.01x2 + -0.01x2 Combine like terms: 200 + -200 = 0 -200 + 11x + -0.01x2 = 0 + -10x + 10x + 0.01x2 + -0.01x2 -200 + 11x + -0.01x2 = -10x + 10x + 0.01x2 + -0.01x2 Combine like terms: -10x + 10x = 0 -200 + 11x + -0.01x2 = 0 + 0.01x2 + -0.01x2 -200 + 11x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -200 + 11x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 20000 + -1100x + x2 = 0 Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -1100x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -1100x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -1100x + x2 = 0 + -20000 -1100x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -1100x + x2 = -20000 The x term is -1100x. Take half its coefficient (-550). Square it (302500) and add it to both sides. Add '302500' to each side of the equation. -1100x + 302500 + x2 = -20000 + 302500 Reorder the terms: 302500 + -1100x + x2 = -20000 + 302500 Combine like terms: -20000 + 302500 = 282500 302500 + -1100x + x2 = 282500 Factor a perfect square on the left side: (x + -550)(x + -550) = 282500 Calculate the square root of the right side: 531.507290637 Break this problem into two subproblems by setting (x + -550) equal to 531.507290637 and -531.507290637.Subproblem 1
x + -550 = 531.507290637 Simplifying x + -550 = 531.507290637 Reorder the terms: -550 + x = 531.507290637 Solving -550 + x = 531.507290637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + x = 531.507290637 + 550 Combine like terms: -550 + 550 = 0 0 + x = 531.507290637 + 550 x = 531.507290637 + 550 Combine like terms: 531.507290637 + 550 = 1081.507290637 x = 1081.507290637 Simplifying x = 1081.507290637Subproblem 2
x + -550 = -531.507290637 Simplifying x + -550 = -531.507290637 Reorder the terms: -550 + x = -531.507290637 Solving -550 + x = -531.507290637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + x = -531.507290637 + 550 Combine like terms: -550 + 550 = 0 0 + x = -531.507290637 + 550 x = -531.507290637 + 550 Combine like terms: -531.507290637 + 550 = 18.492709363 x = 18.492709363 Simplifying x = 18.492709363Solution
The solution to the problem is based on the solutions from the subproblems. x = {1081.507290637, 18.492709363}
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