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Simplifying 200x + -1x2 = 40x + -5500 Reorder the terms: 200x + -1x2 = -5500 + 40x Solving 200x + -1x2 = -5500 + 40x Solving for variable 'x'. Reorder the terms: 5500 + 200x + -40x + -1x2 = -5500 + 40x + 5500 + -40x Combine like terms: 200x + -40x = 160x 5500 + 160x + -1x2 = -5500 + 40x + 5500 + -40x Reorder the terms: 5500 + 160x + -1x2 = -5500 + 5500 + 40x + -40x Combine like terms: -5500 + 5500 = 0 5500 + 160x + -1x2 = 0 + 40x + -40x 5500 + 160x + -1x2 = 40x + -40x Combine like terms: 40x + -40x = 0 5500 + 160x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5500 + -160x + x2 = 0 Move the constant term to the right: Add '5500' to each side of the equation. -5500 + -160x + 5500 + x2 = 0 + 5500 Reorder the terms: -5500 + 5500 + -160x + x2 = 0 + 5500 Combine like terms: -5500 + 5500 = 0 0 + -160x + x2 = 0 + 5500 -160x + x2 = 0 + 5500 Combine like terms: 0 + 5500 = 5500 -160x + x2 = 5500 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = 5500 + 6400 Reorder the terms: 6400 + -160x + x2 = 5500 + 6400 Combine like terms: 5500 + 6400 = 11900 6400 + -160x + x2 = 11900 Factor a perfect square on the left side: (x + -80)(x + -80) = 11900 Calculate the square root of the right side: 109.087121146 Break this problem into two subproblems by setting (x + -80) equal to 109.087121146 and -109.087121146.Subproblem 1
x + -80 = 109.087121146 Simplifying x + -80 = 109.087121146 Reorder the terms: -80 + x = 109.087121146 Solving -80 + x = 109.087121146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 109.087121146 + 80 Combine like terms: -80 + 80 = 0 0 + x = 109.087121146 + 80 x = 109.087121146 + 80 Combine like terms: 109.087121146 + 80 = 189.087121146 x = 189.087121146 Simplifying x = 189.087121146Subproblem 2
x + -80 = -109.087121146 Simplifying x + -80 = -109.087121146 Reorder the terms: -80 + x = -109.087121146 Solving -80 + x = -109.087121146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -109.087121146 + 80 Combine like terms: -80 + 80 = 0 0 + x = -109.087121146 + 80 x = -109.087121146 + 80 Combine like terms: -109.087121146 + 80 = -29.087121146 x = -29.087121146 Simplifying x = -29.087121146Solution
The solution to the problem is based on the solutions from the subproblems. x = {189.087121146, -29.087121146}
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