h^2-8h+3=0

Solution for h^2-8h+3=0 equation:

Simplifying
h2 + -8h + 3 = 0

Reorder the terms:
3 + -8h + h2 = 0

Solving
3 + -8h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8h + -3 + h2 = 0 + -3

Reorder the terms:
3 + -3 + -8h + h2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8h + h2 = 0 + -3
-8h + h2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8h + h2 = -3

The h term is -8h.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8h + 16 + h2 = -3 + 16

Reorder the terms:
16 + -8h + h2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8h + h2 = 13

Factor a perfect square on the left side:
(h + -4)(h + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(h + -4) equal to 3.605551275 and -3.605551275.

Subproblem 1
h + -4 = 3.605551275

Simplifying
h + -4 = 3.605551275

Reorder the terms:
-4 + h = 3.605551275

Solving
-4 + h = 3.605551275

Solving for variable 'h'.

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

Add '4' to each side of the equation.
-4 + 4 + h = 3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + h = 3.605551275 + 4
h = 3.605551275 + 4

Combine like terms: 3.605551275 + 4 = 7.605551275
h = 7.605551275

Simplifying
h = 7.605551275

Subproblem 2
h + -4 = -3.605551275

Simplifying
h + -4 = -3.605551275

Reorder the terms:
-4 + h = -3.605551275

Solving
-4 + h = -3.605551275

Solving for variable 'h'.

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

Add '4' to each side of the equation.
-4 + 4 + h = -3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + h = -3.605551275 + 4
h = -3.605551275 + 4

Combine like terms: -3.605551275 + 4 = 0.394448725
h = 0.394448725

Simplifying
h = 0.394448725

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.605551275, 0.394448725}