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Simplifying x2 + 110x + 2000 = 0 Reorder the terms: 2000 + 110x + x2 = 0 Solving 2000 + 110x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + 110x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + 110x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + 110x + x2 = 0 + -2000 110x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 110x + x2 = -2000 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 = -2000 + 3025 Reorder the terms: 3025 + 110x + x2 = -2000 + 3025 Combine like terms: -2000 + 3025 = 1025 3025 + 110x + x2 = 1025 Factor a perfect square on the left side: (x + 55)(x + 55) = 1025 Calculate the square root of the right side: 32.015621187 Break this problem into two subproblems by setting (x + 55) equal to 32.015621187 and -32.015621187.Subproblem 1
x + 55 = 32.015621187 Simplifying x + 55 = 32.015621187 Reorder the terms: 55 + x = 32.015621187 Solving 55 + x = 32.015621187 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 = 32.015621187 + -55 Combine like terms: 55 + -55 = 0 0 + x = 32.015621187 + -55 x = 32.015621187 + -55 Combine like terms: 32.015621187 + -55 = -22.984378813 x = -22.984378813 Simplifying x = -22.984378813Subproblem 2
x + 55 = -32.015621187 Simplifying x + 55 = -32.015621187 Reorder the terms: 55 + x = -32.015621187 Solving 55 + x = -32.015621187 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 = -32.015621187 + -55 Combine like terms: 55 + -55 = 0 0 + x = -32.015621187 + -55 x = -32.015621187 + -55 Combine like terms: -32.015621187 + -55 = -87.015621187 x = -87.015621187 Simplifying x = -87.015621187Solution
The solution to the problem is based on the solutions from the subproblems. x = {-22.984378813, -87.015621187}
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