4a^2-20a+17=0

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Solution for 4a^2-20a+17=0 equation:


Simplifying
4a2 + -20a + 17 = 0

Reorder the terms:
17 + -20a + 4a2 = 0

Solving
17 + -20a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
4.25 + -5a + a2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + -5a + -4.25 + a2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + -5a + a2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + -5a + a2 = 0 + -4.25
-5a + a2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
-5a + a2 = -4.25

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = -4.25 + 6.25

Reorder the terms:
6.25 + -5a + a2 = -4.25 + 6.25

Combine like terms: -4.25 + 6.25 = 2
6.25 + -5a + a2 = 2

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(a + -2.5) equal to 1.414213562 and -1.414213562.

Subproblem 1

a + -2.5 = 1.414213562 Simplifying a + -2.5 = 1.414213562 Reorder the terms: -2.5 + a = 1.414213562 Solving -2.5 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 1.414213562 + 2.5 a = 1.414213562 + 2.5 Combine like terms: 1.414213562 + 2.5 = 3.914213562 a = 3.914213562 Simplifying a = 3.914213562

Subproblem 2

a + -2.5 = -1.414213562 Simplifying a + -2.5 = -1.414213562 Reorder the terms: -2.5 + a = -1.414213562 Solving -2.5 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -1.414213562 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -1.414213562 + 2.5 a = -1.414213562 + 2.5 Combine like terms: -1.414213562 + 2.5 = 1.085786438 a = 1.085786438 Simplifying a = 1.085786438

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.914213562, 1.085786438}

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