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Simplifying x2 + 110x + -1800 = 0 Reorder the terms: -1800 + 110x + x2 = 0 Solving -1800 + 110x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 110x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 110x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 110x + x2 = 0 + 1800 110x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 110x + x2 = 1800 The x term is 110x. Take half its coefficient (55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. 110x + 3025 + x2 = 1800 + 3025 Reorder the terms: 3025 + 110x + x2 = 1800 + 3025 Combine like terms: 1800 + 3025 = 4825 3025 + 110x + x2 = 4825 Factor a perfect square on the left side: (x + 55)(x + 55) = 4825 Calculate the square root of the right side: 69.462219947 Break this problem into two subproblems by setting (x + 55) equal to 69.462219947 and -69.462219947.Subproblem 1
x + 55 = 69.462219947 Simplifying x + 55 = 69.462219947 Reorder the terms: 55 + x = 69.462219947 Solving 55 + x = 69.462219947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = 69.462219947 + -55 Combine like terms: 55 + -55 = 0 0 + x = 69.462219947 + -55 x = 69.462219947 + -55 Combine like terms: 69.462219947 + -55 = 14.462219947 x = 14.462219947 Simplifying x = 14.462219947Subproblem 2
x + 55 = -69.462219947 Simplifying x + 55 = -69.462219947 Reorder the terms: 55 + x = -69.462219947 Solving 55 + x = -69.462219947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = -69.462219947 + -55 Combine like terms: 55 + -55 = 0 0 + x = -69.462219947 + -55 x = -69.462219947 + -55 Combine like terms: -69.462219947 + -55 = -124.462219947 x = -124.462219947 Simplifying x = -124.462219947Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.462219947, -124.462219947}
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