x^2-16x+62=0

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Solution for x^2-16x+62=0 equation: 


Simplifying
x2 + -16x + 62 = 0

Reorder the terms:
62 + -16x + x2 = 0

Solving
62 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-62' to each side of the equation.
62 + -16x + -62 + x2 = 0 + -62

Reorder the terms:
62 + -62 + -16x + x2 = 0 + -62

Combine like terms: 62 + -62 = 0
0 + -16x + x2 = 0 + -62
-16x + x2 = 0 + -62

Combine like terms: 0 + -62 = -62
-16x + x2 = -62

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 = -62 + 64

Reorder the terms:
64 + -16x + x2 = -62 + 64

Combine like terms: -62 + 64 = 2
64 + -16x + x2 = 2

Factor a perfect square on the left side:
(x + -8)(x + -8) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -8) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -8 = 1.414213562

Simplifying
x + -8 = 1.414213562

Reorder the terms:
-8 + x = 1.414213562

Solving
-8 + x = 1.414213562

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 = 1.414213562 + 8

Combine like terms: -8 + 8 = 0
0 + x = 1.414213562 + 8
x = 1.414213562 + 8

Combine like terms: 1.414213562 + 8 = 9.414213562
x = 9.414213562

Simplifying
x = 9.414213562


Subproblem 2
x + -8 = -1.414213562

Simplifying
x + -8 = -1.414213562

Reorder the terms:
-8 + x = -1.414213562

Solving
-8 + x = -1.414213562

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 = -1.414213562 + 8

Combine like terms: -8 + 8 = 0
0 + x = -1.414213562 + 8
x = -1.414213562 + 8

Combine like terms: -1.414213562 + 8 = 6.585786438
x = 6.585786438

Simplifying
x = 6.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.414213562, 6.585786438}

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