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Simplifying x2 + 110x + 14 = 0 Reorder the terms: 14 + 110x + x2 = 0 Solving 14 + 110x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 110x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 110x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 110x + x2 = 0 + -14 110x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 110x + x2 = -14 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 = -14 + 3025 Reorder the terms: 3025 + 110x + x2 = -14 + 3025 Combine like terms: -14 + 3025 = 3011 3025 + 110x + x2 = 3011 Factor a perfect square on the left side: (x + 55)(x + 55) = 3011 Calculate the square root of the right side: 54.872579673 Break this problem into two subproblems by setting (x + 55) equal to 54.872579673 and -54.872579673.Subproblem 1
x + 55 = 54.872579673 Simplifying x + 55 = 54.872579673 Reorder the terms: 55 + x = 54.872579673 Solving 55 + x = 54.872579673 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 = 54.872579673 + -55 Combine like terms: 55 + -55 = 0 0 + x = 54.872579673 + -55 x = 54.872579673 + -55 Combine like terms: 54.872579673 + -55 = -0.127420327 x = -0.127420327 Simplifying x = -0.127420327Subproblem 2
x + 55 = -54.872579673 Simplifying x + 55 = -54.872579673 Reorder the terms: 55 + x = -54.872579673 Solving 55 + x = -54.872579673 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 = -54.872579673 + -55 Combine like terms: 55 + -55 = 0 0 + x = -54.872579673 + -55 x = -54.872579673 + -55 Combine like terms: -54.872579673 + -55 = -109.872579673 x = -109.872579673 Simplifying x = -109.872579673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.127420327, -109.872579673}
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