a^2-7a+5=0

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Solution for a^2-7a+5=0 equation: 


Simplifying
a2 + -7a + 5 = 0

Reorder the terms:
5 + -7a + a2 = 0

Solving
5 + -7a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -7a + -5 + a2 = 0 + -5

Reorder the terms:
5 + -5 + -7a + a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7a + a2 = 0 + -5
-7a + a2 = 0 + -5

Combine like terms: 0 + -5 = -5
-7a + a2 = -5

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = -5 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -5 + 12.25

Combine like terms: -5 + 12.25 = 7.25
12.25 + -7a + a2 = 7.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(a + -3.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
a + -3.5 = 2.692582404

Simplifying
a + -3.5 = 2.692582404

Reorder the terms:
-3.5 + a = 2.692582404

Solving
-3.5 + a = 2.692582404

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = 2.692582404 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = 2.692582404 + 3.5
a = 2.692582404 + 3.5

Combine like terms: 2.692582404 + 3.5 = 6.192582404
a = 6.192582404

Simplifying
a = 6.192582404


Subproblem 2
a + -3.5 = -2.692582404

Simplifying
a + -3.5 = -2.692582404

Reorder the terms:
-3.5 + a = -2.692582404

Solving
-3.5 + a = -2.692582404

Solving for variable 'a'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + a = -2.692582404 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + a = -2.692582404 + 3.5
a = -2.692582404 + 3.5

Combine like terms: -2.692582404 + 3.5 = 0.807417596
a = 0.807417596

Simplifying
a = 0.807417596


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.192582404, 0.807417596}

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