x^2-54x+240=0

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Solution for x^2-54x+240=0 equation:


Simplifying
x2 + -54x + 240 = 0

Reorder the terms:
240 + -54x + x2 = 0

Solving
240 + -54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -54x + -240 + x2 = 0 + -240

Reorder the terms:
240 + -240 + -54x + x2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -54x + x2 = 0 + -240
-54x + x2 = 0 + -240

Combine like terms: 0 + -240 = -240
-54x + x2 = -240

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 = -240 + 729

Reorder the terms:
729 + -54x + x2 = -240 + 729

Combine like terms: -240 + 729 = 489
729 + -54x + x2 = 489

Factor a perfect square on the left side:
(x + -27)(x + -27) = 489

Calculate the square root of the right side: 22.113344387

Break this problem into two subproblems by setting 
(x + -27) equal to 22.113344387 and -22.113344387.

Subproblem 1

x + -27 = 22.113344387 Simplifying x + -27 = 22.113344387 Reorder the terms: -27 + x = 22.113344387 Solving -27 + x = 22.113344387 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 = 22.113344387 + 27 Combine like terms: -27 + 27 = 0 0 + x = 22.113344387 + 27 x = 22.113344387 + 27 Combine like terms: 22.113344387 + 27 = 49.113344387 x = 49.113344387 Simplifying x = 49.113344387

Subproblem 2

x + -27 = -22.113344387 Simplifying x + -27 = -22.113344387 Reorder the terms: -27 + x = -22.113344387 Solving -27 + x = -22.113344387 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 = -22.113344387 + 27 Combine like terms: -27 + 27 = 0 0 + x = -22.113344387 + 27 x = -22.113344387 + 27 Combine like terms: -22.113344387 + 27 = 4.886655613 x = 4.886655613 Simplifying x = 4.886655613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.113344387, 4.886655613}

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