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Simplifying x2 + 16 = -110x Reorder the terms: 16 + x2 = -110x Solving 16 + x2 = -110x Solving for variable 'x'. Reorder the terms: 16 + 110x + x2 = -110x + 110x Combine like terms: -110x + 110x = 0 16 + 110x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 110x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 110x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 110x + x2 = 0 + -16 110x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 110x + x2 = -16 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 = -16 + 3025 Reorder the terms: 3025 + 110x + x2 = -16 + 3025 Combine like terms: -16 + 3025 = 3009 3025 + 110x + x2 = 3009 Factor a perfect square on the left side: (x + 55)(x + 55) = 3009 Calculate the square root of the right side: 54.854352608 Break this problem into two subproblems by setting (x + 55) equal to 54.854352608 and -54.854352608.Subproblem 1
x + 55 = 54.854352608 Simplifying x + 55 = 54.854352608 Reorder the terms: 55 + x = 54.854352608 Solving 55 + x = 54.854352608 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 = 54.854352608 + -55 Combine like terms: 55 + -55 = 0 0 + x = 54.854352608 + -55 x = 54.854352608 + -55 Combine like terms: 54.854352608 + -55 = -0.145647392 x = -0.145647392 Simplifying x = -0.145647392Subproblem 2
x + 55 = -54.854352608 Simplifying x + 55 = -54.854352608 Reorder the terms: 55 + x = -54.854352608 Solving 55 + x = -54.854352608 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 = -54.854352608 + -55 Combine like terms: 55 + -55 = 0 0 + x = -54.854352608 + -55 x = -54.854352608 + -55 Combine like terms: -54.854352608 + -55 = -109.854352608 x = -109.854352608 Simplifying x = -109.854352608Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.145647392, -109.854352608}
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