a^2-10a+4=0

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Solution for a^2-10a+4=0 equation: 


Simplifying
a2 + -10a + 4 = 0

Reorder the terms:
4 + -10a + a2 = 0

Solving
4 + -10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -10a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + -10a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -10a + a2 = 0 + -4
-10a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
-10a + a2 = -4

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = -4 + 25

Reorder the terms:
25 + -10a + a2 = -4 + 25

Combine like terms: -4 + 25 = 21
25 + -10a + a2 = 21

Factor a perfect square on the left side:
(a + -5)(a + -5) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(a + -5) equal to 4.582575695 and -4.582575695.


Subproblem 1
a + -5 = 4.582575695

Simplifying
a + -5 = 4.582575695

Reorder the terms:
-5 + a = 4.582575695

Solving
-5 + a = 4.582575695

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = 4.582575695 + 5

Combine like terms: -5 + 5 = 0
0 + a = 4.582575695 + 5
a = 4.582575695 + 5

Combine like terms: 4.582575695 + 5 = 9.582575695
a = 9.582575695

Simplifying
a = 9.582575695


Subproblem 2
a + -5 = -4.582575695

Simplifying
a + -5 = -4.582575695

Reorder the terms:
-5 + a = -4.582575695

Solving
-5 + a = -4.582575695

Solving for variable 'a'.

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

Add '5' to each side of the equation.
-5 + 5 + a = -4.582575695 + 5

Combine like terms: -5 + 5 = 0
0 + a = -4.582575695 + 5
a = -4.582575695 + 5

Combine like terms: -4.582575695 + 5 = 0.417424305
a = 0.417424305

Simplifying
a = 0.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {9.582575695, 0.417424305}

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