x^2-54x+404=0

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Solution for x^2-54x+404=0 equation:


Simplifying
x2 + -54x + 404 = 0

Reorder the terms:
404 + -54x + x2 = 0

Solving
404 + -54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-404' to each side of the equation.
404 + -54x + -404 + x2 = 0 + -404

Reorder the terms:
404 + -404 + -54x + x2 = 0 + -404

Combine like terms: 404 + -404 = 0
0 + -54x + x2 = 0 + -404
-54x + x2 = 0 + -404

Combine like terms: 0 + -404 = -404
-54x + x2 = -404

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 = -404 + 729

Reorder the terms:
729 + -54x + x2 = -404 + 729

Combine like terms: -404 + 729 = 325
729 + -54x + x2 = 325

Factor a perfect square on the left side:
(x + -27)(x + -27) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + -27) equal to 18.027756377 and -18.027756377.

Subproblem 1

x + -27 = 18.027756377 Simplifying x + -27 = 18.027756377 Reorder the terms: -27 + x = 18.027756377 Solving -27 + x = 18.027756377 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 = 18.027756377 + 27 Combine like terms: -27 + 27 = 0 0 + x = 18.027756377 + 27 x = 18.027756377 + 27 Combine like terms: 18.027756377 + 27 = 45.027756377 x = 45.027756377 Simplifying x = 45.027756377

Subproblem 2

x + -27 = -18.027756377 Simplifying x + -27 = -18.027756377 Reorder the terms: -27 + x = -18.027756377 Solving -27 + x = -18.027756377 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 = -18.027756377 + 27 Combine like terms: -27 + 27 = 0 0 + x = -18.027756377 + 27 x = -18.027756377 + 27 Combine like terms: -18.027756377 + 27 = 8.972243623 x = 8.972243623 Simplifying x = 8.972243623

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.027756377, 8.972243623}

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