x^2-44x+120=0

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Solution for x^2-44x+120=0 equation:


Simplifying
x2 + -44x + 120 = 0

Reorder the terms:
120 + -44x + x2 = 0

Solving
120 + -44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -44x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -44x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -44x + x2 = 0 + -120
-44x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-44x + x2 = -120

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -120 + 484

Reorder the terms:
484 + -44x + x2 = -120 + 484

Combine like terms: -120 + 484 = 364
484 + -44x + x2 = 364

Factor a perfect square on the left side:
(x + -22)(x + -22) = 364

Calculate the square root of the right side: 19.078784028

Break this problem into two subproblems by setting 
(x + -22) equal to 19.078784028 and -19.078784028.

Subproblem 1

x + -22 = 19.078784028 Simplifying x + -22 = 19.078784028 Reorder the terms: -22 + x = 19.078784028 Solving -22 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 19.078784028 + 22 Combine like terms: -22 + 22 = 0 0 + x = 19.078784028 + 22 x = 19.078784028 + 22 Combine like terms: 19.078784028 + 22 = 41.078784028 x = 41.078784028 Simplifying x = 41.078784028

Subproblem 2

x + -22 = -19.078784028 Simplifying x + -22 = -19.078784028 Reorder the terms: -22 + x = -19.078784028 Solving -22 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -19.078784028 + 22 Combine like terms: -22 + 22 = 0 0 + x = -19.078784028 + 22 x = -19.078784028 + 22 Combine like terms: -19.078784028 + 22 = 2.921215972 x = 2.921215972 Simplifying x = 2.921215972

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.078784028, 2.921215972}

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