x^2-16x+46=0

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Solution for x^2-16x+46=0 equation: 


Simplifying
x2 + -16x + 46 = 0

Reorder the terms:
46 + -16x + x2 = 0

Solving
46 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -16x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + -16x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -16x + x2 = 0 + -46
-16x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
-16x + x2 = -46

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -46 + 64

Reorder the terms:
64 + -16x + x2 = -46 + 64

Combine like terms: -46 + 64 = 18
64 + -16x + x2 = 18

Factor a perfect square on the left side:
(x + -8)(x + -8) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -8) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -8 = 4.242640687

Simplifying
x + -8 = 4.242640687

Reorder the terms:
-8 + x = 4.242640687

Solving
-8 + x = 4.242640687

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + x = 4.242640687 + 8

Combine like terms: -8 + 8 = 0
0 + x = 4.242640687 + 8
x = 4.242640687 + 8

Combine like terms: 4.242640687 + 8 = 12.242640687
x = 12.242640687

Simplifying
x = 12.242640687


Subproblem 2
x + -8 = -4.242640687

Simplifying
x + -8 = -4.242640687

Reorder the terms:
-8 + x = -4.242640687

Solving
-8 + x = -4.242640687

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + x = -4.242640687 + 8

Combine like terms: -8 + 8 = 0
0 + x = -4.242640687 + 8
x = -4.242640687 + 8

Combine like terms: -4.242640687 + 8 = 3.757359313
x = 3.757359313

Simplifying
x = 3.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.242640687, 3.757359313}

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