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Simplifying 385 = 25x + -0.2x2 Solving 385 = 25x + -0.2x2 Solving for variable 'x'. Reorder the terms: 385 + -25x + 0.2x2 = 25x + -25x + -0.2x2 + 0.2x2 Combine like terms: 25x + -25x = 0 385 + -25x + 0.2x2 = 0 + -0.2x2 + 0.2x2 385 + -25x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 385 + -25x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 1925 + -125x + x2 = 0 Move the constant term to the right: Add '-1925' to each side of the equation. 1925 + -125x + -1925 + x2 = 0 + -1925 Reorder the terms: 1925 + -1925 + -125x + x2 = 0 + -1925 Combine like terms: 1925 + -1925 = 0 0 + -125x + x2 = 0 + -1925 -125x + x2 = 0 + -1925 Combine like terms: 0 + -1925 = -1925 -125x + x2 = -1925 The x term is -125x. Take half its coefficient (-62.5). Square it (3906.25) and add it to both sides. Add '3906.25' to each side of the equation. -125x + 3906.25 + x2 = -1925 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = -1925 + 3906.25 Combine like terms: -1925 + 3906.25 = 1981.25 3906.25 + -125x + x2 = 1981.25 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 1981.25 Calculate the square root of the right side: 44.511234537 Break this problem into two subproblems by setting (x + -62.5) equal to 44.511234537 and -44.511234537.Subproblem 1
x + -62.5 = 44.511234537 Simplifying x + -62.5 = 44.511234537 Reorder the terms: -62.5 + x = 44.511234537 Solving -62.5 + x = 44.511234537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = 44.511234537 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 44.511234537 + 62.5 x = 44.511234537 + 62.5 Combine like terms: 44.511234537 + 62.5 = 107.011234537 x = 107.011234537 Simplifying x = 107.011234537Subproblem 2
x + -62.5 = -44.511234537 Simplifying x + -62.5 = -44.511234537 Reorder the terms: -62.5 + x = -44.511234537 Solving -62.5 + x = -44.511234537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = -44.511234537 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -44.511234537 + 62.5 x = -44.511234537 + 62.5 Combine like terms: -44.511234537 + 62.5 = 17.988765463 x = 17.988765463 Simplifying x = 17.988765463Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.011234537, 17.988765463}
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