2a^2-13a+17=0

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Solution for 2a^2-13a+17=0 equation:


Simplifying
2a2 + -13a + 17 = 0

Reorder the terms:
17 + -13a + 2a2 = 0

Solving
17 + -13a + 2a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
8.5 + -6.5a + a2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -6.5a + -8.5 + a2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -6.5a + a2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -6.5a + a2 = 0 + -8.5
-6.5a + a2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-6.5a + a2 = -8.5

The a term is -6.5a.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5a + 10.5625 + a2 = -8.5 + 10.5625

Reorder the terms:
10.5625 + -6.5a + a2 = -8.5 + 10.5625

Combine like terms: -8.5 + 10.5625 = 2.0625
10.5625 + -6.5a + a2 = 2.0625

Factor a perfect square on the left side:
(a + -3.25)(a + -3.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(a + -3.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

a + -3.25 = 1.436140662 Simplifying a + -3.25 = 1.436140662 Reorder the terms: -3.25 + a = 1.436140662 Solving -3.25 + a = 1.436140662 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = 1.436140662 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = 1.436140662 + 3.25 a = 1.436140662 + 3.25 Combine like terms: 1.436140662 + 3.25 = 4.686140662 a = 4.686140662 Simplifying a = 4.686140662

Subproblem 2

a + -3.25 = -1.436140662 Simplifying a + -3.25 = -1.436140662 Reorder the terms: -3.25 + a = -1.436140662 Solving -3.25 + a = -1.436140662 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = -1.436140662 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = -1.436140662 + 3.25 a = -1.436140662 + 3.25 Combine like terms: -1.436140662 + 3.25 = 1.813859338 a = 1.813859338 Simplifying a = 1.813859338

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.686140662, 1.813859338}

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