x^2-54x+624=0

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Solution for x^2-54x+624=0 equation:


Simplifying
x2 + -54x + 624 = 0

Reorder the terms:
624 + -54x + x2 = 0

Solving
624 + -54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-624' to each side of the equation.
624 + -54x + -624 + x2 = 0 + -624

Reorder the terms:
624 + -624 + -54x + x2 = 0 + -624

Combine like terms: 624 + -624 = 0
0 + -54x + x2 = 0 + -624
-54x + x2 = 0 + -624

Combine like terms: 0 + -624 = -624
-54x + x2 = -624

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 = -624 + 729

Reorder the terms:
729 + -54x + x2 = -624 + 729

Combine like terms: -624 + 729 = 105
729 + -54x + x2 = 105

Factor a perfect square on the left side:
(x + -27)(x + -27) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(x + -27) equal to 10.246950766 and -10.246950766.

Subproblem 1

x + -27 = 10.246950766 Simplifying x + -27 = 10.246950766 Reorder the terms: -27 + x = 10.246950766 Solving -27 + x = 10.246950766 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 = 10.246950766 + 27 Combine like terms: -27 + 27 = 0 0 + x = 10.246950766 + 27 x = 10.246950766 + 27 Combine like terms: 10.246950766 + 27 = 37.246950766 x = 37.246950766 Simplifying x = 37.246950766

Subproblem 2

x + -27 = -10.246950766 Simplifying x + -27 = -10.246950766 Reorder the terms: -27 + x = -10.246950766 Solving -27 + x = -10.246950766 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 = -10.246950766 + 27 Combine like terms: -27 + 27 = 0 0 + x = -10.246950766 + 27 x = -10.246950766 + 27 Combine like terms: -10.246950766 + 27 = 16.753049234 x = 16.753049234 Simplifying x = 16.753049234

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.246950766, 16.753049234}

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