x^2+54x+486=0

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Solution for x^2+54x+486=0 equation:


Simplifying
x2 + 54x + 486 = 0

Reorder the terms:
486 + 54x + x2 = 0

Solving
486 + 54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-486' to each side of the equation.
486 + 54x + -486 + x2 = 0 + -486

Reorder the terms:
486 + -486 + 54x + x2 = 0 + -486

Combine like terms: 486 + -486 = 0
0 + 54x + x2 = 0 + -486
54x + x2 = 0 + -486

Combine like terms: 0 + -486 = -486
54x + x2 = -486

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 = -486 + 729

Reorder the terms:
729 + 54x + x2 = -486 + 729

Combine like terms: -486 + 729 = 243
729 + 54x + x2 = 243

Factor a perfect square on the left side:
(x + 27)(x + 27) = 243

Calculate the square root of the right side: 15.588457268

Break this problem into two subproblems by setting 
(x + 27) equal to 15.588457268 and -15.588457268.

Subproblem 1

x + 27 = 15.588457268 Simplifying x + 27 = 15.588457268 Reorder the terms: 27 + x = 15.588457268 Solving 27 + x = 15.588457268 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 = 15.588457268 + -27 Combine like terms: 27 + -27 = 0 0 + x = 15.588457268 + -27 x = 15.588457268 + -27 Combine like terms: 15.588457268 + -27 = -11.411542732 x = -11.411542732 Simplifying x = -11.411542732

Subproblem 2

x + 27 = -15.588457268 Simplifying x + 27 = -15.588457268 Reorder the terms: 27 + x = -15.588457268 Solving 27 + x = -15.588457268 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 = -15.588457268 + -27 Combine like terms: 27 + -27 = 0 0 + x = -15.588457268 + -27 x = -15.588457268 + -27 Combine like terms: -15.588457268 + -27 = -42.588457268 x = -42.588457268 Simplifying x = -42.588457268

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-11.411542732, -42.588457268}

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