x^2-16x+4=0

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Solution for x^2-16x+4=0 equation:


Simplifying
x2 + -16x + 4 = 0

Reorder the terms:
4 + -16x + x2 = 0

Solving
4 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -16x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -16x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -16x + x2 = 0 + -4
-16x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-16x + x2 = -4

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 = -4 + 64

Reorder the terms:
64 + -16x + x2 = -4 + 64

Combine like terms: -4 + 64 = 60
64 + -16x + x2 = 60

Factor a perfect square on the left side:
(x + -8)(x + -8) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + -8) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + -8 = 7.745966692

Simplifying
x + -8 = 7.745966692

Reorder the terms:
-8 + x = 7.745966692

Solving
-8 + x = 7.745966692

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 = 7.745966692 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.745966692 + 8
x = 7.745966692 + 8

Combine like terms: 7.745966692 + 8 = 15.745966692
x = 15.745966692

Simplifying
x = 15.745966692


Subproblem 2
x + -8 = -7.745966692

Simplifying
x + -8 = -7.745966692

Reorder the terms:
-8 + x = -7.745966692

Solving
-8 + x = -7.745966692

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 = -7.745966692 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.745966692 + 8
x = -7.745966692 + 8

Combine like terms: -7.745966692 + 8 = 0.254033308
x = 0.254033308

Simplifying
x = 0.254033308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.745966692, 0.254033308}

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