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Simplifying 220x + -1x2 = 50x + 2600 Reorder the terms: 220x + -1x2 = 2600 + 50x Solving 220x + -1x2 = 2600 + 50x Solving for variable 'x'. Reorder the terms: -2600 + 220x + -50x + -1x2 = 2600 + 50x + -2600 + -50x Combine like terms: 220x + -50x = 170x -2600 + 170x + -1x2 = 2600 + 50x + -2600 + -50x Reorder the terms: -2600 + 170x + -1x2 = 2600 + -2600 + 50x + -50x Combine like terms: 2600 + -2600 = 0 -2600 + 170x + -1x2 = 0 + 50x + -50x -2600 + 170x + -1x2 = 50x + -50x Combine like terms: 50x + -50x = 0 -2600 + 170x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2600 + -170x + x2 = 0 Move the constant term to the right: Add '-2600' to each side of the equation. 2600 + -170x + -2600 + x2 = 0 + -2600 Reorder the terms: 2600 + -2600 + -170x + x2 = 0 + -2600 Combine like terms: 2600 + -2600 = 0 0 + -170x + x2 = 0 + -2600 -170x + x2 = 0 + -2600 Combine like terms: 0 + -2600 = -2600 -170x + x2 = -2600 The x term is -170x. Take half its coefficient (-85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. -170x + 7225 + x2 = -2600 + 7225 Reorder the terms: 7225 + -170x + x2 = -2600 + 7225 Combine like terms: -2600 + 7225 = 4625 7225 + -170x + x2 = 4625 Factor a perfect square on the left side: (x + -85)(x + -85) = 4625 Calculate the square root of the right side: 68.007352544 Break this problem into two subproblems by setting (x + -85) equal to 68.007352544 and -68.007352544.Subproblem 1
x + -85 = 68.007352544 Simplifying x + -85 = 68.007352544 Reorder the terms: -85 + x = 68.007352544 Solving -85 + x = 68.007352544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = 68.007352544 + 85 Combine like terms: -85 + 85 = 0 0 + x = 68.007352544 + 85 x = 68.007352544 + 85 Combine like terms: 68.007352544 + 85 = 153.007352544 x = 153.007352544 Simplifying x = 153.007352544Subproblem 2
x + -85 = -68.007352544 Simplifying x + -85 = -68.007352544 Reorder the terms: -85 + x = -68.007352544 Solving -85 + x = -68.007352544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = -68.007352544 + 85 Combine like terms: -85 + 85 = 0 0 + x = -68.007352544 + 85 x = -68.007352544 + 85 Combine like terms: -68.007352544 + 85 = 16.992647456 x = 16.992647456 Simplifying x = 16.992647456Solution
The solution to the problem is based on the solutions from the subproblems. x = {153.007352544, 16.992647456}
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