a^2-13a+10=0

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Solution for a^2-13a+10=0 equation:


Simplifying
a2 + -13a + 10 = 0

Reorder the terms:
10 + -13a + a2 = 0

Solving
10 + -13a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -13a + -10 + a2 = 0 + -10

Reorder the terms:
10 + -10 + -13a + a2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -13a + a2 = 0 + -10
-13a + a2 = 0 + -10

Combine like terms: 0 + -10 = -10
-13a + a2 = -10

The a term is -13a.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13a + 42.25 + a2 = -10 + 42.25

Reorder the terms:
42.25 + -13a + a2 = -10 + 42.25

Combine like terms: -10 + 42.25 = 32.25
42.25 + -13a + a2 = 32.25

Factor a perfect square on the left side:
(a + -6.5)(a + -6.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(a + -6.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

a + -6.5 = 5.678908346 Simplifying a + -6.5 = 5.678908346 Reorder the terms: -6.5 + a = 5.678908346 Solving -6.5 + a = 5.678908346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = 5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = 5.678908346 + 6.5 a = 5.678908346 + 6.5 Combine like terms: 5.678908346 + 6.5 = 12.178908346 a = 12.178908346 Simplifying a = 12.178908346

Subproblem 2

a + -6.5 = -5.678908346 Simplifying a + -6.5 = -5.678908346 Reorder the terms: -6.5 + a = -5.678908346 Solving -6.5 + a = -5.678908346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + a = -5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + a = -5.678908346 + 6.5 a = -5.678908346 + 6.5 Combine like terms: -5.678908346 + 6.5 = 0.821091654 a = 0.821091654 Simplifying a = 0.821091654

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.178908346, 0.821091654}

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