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Simplifying 41x2 + 200x + -36000 = 0 Reorder the terms: -36000 + 200x + 41x2 = 0 Solving -36000 + 200x + 41x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -878.0487805 + 4.87804878x + x2 = 0 Move the constant term to the right: Add '878.0487805' to each side of the equation. -878.0487805 + 4.87804878x + 878.0487805 + x2 = 0 + 878.0487805 Reorder the terms: -878.0487805 + 878.0487805 + 4.87804878x + x2 = 0 + 878.0487805 Combine like terms: -878.0487805 + 878.0487805 = 0.0000000 0.0000000 + 4.87804878x + x2 = 0 + 878.0487805 4.87804878x + x2 = 0 + 878.0487805 Combine like terms: 0 + 878.0487805 = 878.0487805 4.87804878x + x2 = 878.0487805 The x term is 4.87804878x. Take half its coefficient (2.43902439). Square it (5.948839975) and add it to both sides. Add '5.948839975' to each side of the equation. 4.87804878x + 5.948839975 + x2 = 878.0487805 + 5.948839975 Reorder the terms: 5.948839975 + 4.87804878x + x2 = 878.0487805 + 5.948839975 Combine like terms: 878.0487805 + 5.948839975 = 883.997620475 5.948839975 + 4.87804878x + x2 = 883.997620475 Factor a perfect square on the left side: (x + 2.43902439)(x + 2.43902439) = 883.997620475 Calculate the square root of the right side: 29.732097479 Break this problem into two subproblems by setting (x + 2.43902439) equal to 29.732097479 and -29.732097479.Subproblem 1
x + 2.43902439 = 29.732097479 Simplifying x + 2.43902439 = 29.732097479 Reorder the terms: 2.43902439 + x = 29.732097479 Solving 2.43902439 + x = 29.732097479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.43902439' to each side of the equation. 2.43902439 + -2.43902439 + x = 29.732097479 + -2.43902439 Combine like terms: 2.43902439 + -2.43902439 = 0.00000000 0.00000000 + x = 29.732097479 + -2.43902439 x = 29.732097479 + -2.43902439 Combine like terms: 29.732097479 + -2.43902439 = 27.293073089 x = 27.293073089 Simplifying x = 27.293073089Subproblem 2
x + 2.43902439 = -29.732097479 Simplifying x + 2.43902439 = -29.732097479 Reorder the terms: 2.43902439 + x = -29.732097479 Solving 2.43902439 + x = -29.732097479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.43902439' to each side of the equation. 2.43902439 + -2.43902439 + x = -29.732097479 + -2.43902439 Combine like terms: 2.43902439 + -2.43902439 = 0.00000000 0.00000000 + x = -29.732097479 + -2.43902439 x = -29.732097479 + -2.43902439 Combine like terms: -29.732097479 + -2.43902439 = -32.171121869 x = -32.171121869 Simplifying x = -32.171121869Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.293073089, -32.171121869}
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