x^2+54x+55=

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Solution for x^2+54x+55= equation:


Simplifying
x2 + 54x + 55 = 0

Reorder the terms:
55 + 54x + x2 = 0

Solving
55 + 54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-55' to each side of the equation.
55 + 54x + -55 + x2 = 0 + -55

Reorder the terms:
55 + -55 + 54x + x2 = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 54x + x2 = 0 + -55
54x + x2 = 0 + -55

Combine like terms: 0 + -55 = -55
54x + x2 = -55

The x term is 54x.  Take half its coefficient (27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
54x + 729 + x2 = -55 + 729

Reorder the terms:
729 + 54x + x2 = -55 + 729

Combine like terms: -55 + 729 = 674
729 + 54x + x2 = 674

Factor a perfect square on the left side:
(x + 27)(x + 27) = 674

Calculate the square root of the right side: 25.961509971

Break this problem into two subproblems by setting 
(x + 27) equal to 25.961509971 and -25.961509971.

Subproblem 1

x + 27 = 25.961509971 Simplifying x + 27 = 25.961509971 Reorder the terms: 27 + x = 25.961509971 Solving 27 + x = 25.961509971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 25.961509971 + -27 Combine like terms: 27 + -27 = 0 0 + x = 25.961509971 + -27 x = 25.961509971 + -27 Combine like terms: 25.961509971 + -27 = -1.038490029 x = -1.038490029 Simplifying x = -1.038490029

Subproblem 2

x + 27 = -25.961509971 Simplifying x + 27 = -25.961509971 Reorder the terms: 27 + x = -25.961509971 Solving 27 + x = -25.961509971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -25.961509971 + -27 Combine like terms: 27 + -27 = 0 0 + x = -25.961509971 + -27 x = -25.961509971 + -27 Combine like terms: -25.961509971 + -27 = -52.961509971 x = -52.961509971 Simplifying x = -52.961509971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.038490029, -52.961509971}

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