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Simplifying 4996.40(x) = 0.1x2 + 4x + 200 Reorder the terms: 4996.40x = 200 + 4x + 0.1x2 Solving 4996.40x = 200 + 4x + 0.1x2 Solving for variable 'x'. Reorder the terms: -200 + 4996.40x + -4x + -0.1x2 = 200 + 4x + 0.1x2 + -200 + -4x + -0.1x2 Combine like terms: 4996.40x + -4x = 4992.4x -200 + 4992.4x + -0.1x2 = 200 + 4x + 0.1x2 + -200 + -4x + -0.1x2 Reorder the terms: -200 + 4992.4x + -0.1x2 = 200 + -200 + 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 200 + -200 = 0 -200 + 4992.4x + -0.1x2 = 0 + 4x + -4x + 0.1x2 + -0.1x2 -200 + 4992.4x + -0.1x2 = 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 4x + -4x = 0 -200 + 4992.4x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -200 + 4992.4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -200 + 4992.4x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 2000 + -49924x + x2 = 0 Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -49924x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -49924x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -49924x + x2 = 0 + -2000 -49924x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -49924x + x2 = -2000 The x term is -49924x. Take half its coefficient (-24962). Square it (623101444) and add it to both sides. Add '623101444' to each side of the equation. -49924x + 623101444 + x2 = -2000 + 623101444 Reorder the terms: 623101444 + -49924x + x2 = -2000 + 623101444 Combine like terms: -2000 + 623101444 = 623099444 623101444 + -49924x + x2 = 623099444 Factor a perfect square on the left side: (x + -24962)(x + -24962) = 623099444 Calculate the square root of the right side: 24961.959939075 Break this problem into two subproblems by setting (x + -24962) equal to 24961.959939075 and -24961.959939075.Subproblem 1
x + -24962 = 24961.959939075 Simplifying x + -24962 = 24961.959939075 Reorder the terms: -24962 + x = 24961.959939075 Solving -24962 + x = 24961.959939075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24962' to each side of the equation. -24962 + 24962 + x = 24961.959939075 + 24962 Combine like terms: -24962 + 24962 = 0 0 + x = 24961.959939075 + 24962 x = 24961.959939075 + 24962 Combine like terms: 24961.959939075 + 24962 = 49923.959939075 x = 49923.959939075 Simplifying x = 49923.959939075Subproblem 2
x + -24962 = -24961.959939075 Simplifying x + -24962 = -24961.959939075 Reorder the terms: -24962 + x = -24961.959939075 Solving -24962 + x = -24961.959939075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24962' to each side of the equation. -24962 + 24962 + x = -24961.959939075 + 24962 Combine like terms: -24962 + 24962 = 0 0 + x = -24961.959939075 + 24962 x = -24961.959939075 + 24962 Combine like terms: -24961.959939075 + 24962 = 0.040060925 x = 0.040060925 Simplifying x = 0.040060925Solution
The solution to the problem is based on the solutions from the subproblems. x = {49923.959939075, 0.040060925}
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