x^2-46x+120=0

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Solution for x^2-46x+120=0 equation:


Simplifying
x2 + -46x + 120 = 0

Reorder the terms:
120 + -46x + x2 = 0

Solving
120 + -46x + 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 + -46x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -46x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -46x + x2 = 0 + -120
-46x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-46x + x2 = -120

The x term is -46x.  Take half its coefficient (-23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
-46x + 529 + x2 = -120 + 529

Reorder the terms:
529 + -46x + x2 = -120 + 529

Combine like terms: -120 + 529 = 409
529 + -46x + x2 = 409

Factor a perfect square on the left side:
(x + -23)(x + -23) = 409

Calculate the square root of the right side: 20.223748416

Break this problem into two subproblems by setting 
(x + -23) equal to 20.223748416 and -20.223748416.

Subproblem 1

x + -23 = 20.223748416 Simplifying x + -23 = 20.223748416 Reorder the terms: -23 + x = 20.223748416 Solving -23 + x = 20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 20.223748416 + 23 Combine like terms: -23 + 23 = 0 0 + x = 20.223748416 + 23 x = 20.223748416 + 23 Combine like terms: 20.223748416 + 23 = 43.223748416 x = 43.223748416 Simplifying x = 43.223748416

Subproblem 2

x + -23 = -20.223748416 Simplifying x + -23 = -20.223748416 Reorder the terms: -23 + x = -20.223748416 Solving -23 + x = -20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -20.223748416 + 23 Combine like terms: -23 + 23 = 0 0 + x = -20.223748416 + 23 x = -20.223748416 + 23 Combine like terms: -20.223748416 + 23 = 2.776251584 x = 2.776251584 Simplifying x = 2.776251584

Solution

The solution to the problem is based on the solutions from the subproblems. x = {43.223748416, 2.776251584}

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