a^2-20a+39=0

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Solution for a^2-20a+39=0 equation:


Simplifying
a2 + -20a + 39 = 0

Reorder the terms:
39 + -20a + a2 = 0

Solving
39 + -20a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -20a + -39 + a2 = 0 + -39

Reorder the terms:
39 + -39 + -20a + a2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -20a + a2 = 0 + -39
-20a + a2 = 0 + -39

Combine like terms: 0 + -39 = -39
-20a + a2 = -39

The a term is -20a.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20a + 100 + a2 = -39 + 100

Reorder the terms:
100 + -20a + a2 = -39 + 100

Combine like terms: -39 + 100 = 61
100 + -20a + a2 = 61

Factor a perfect square on the left side:
(a + -10)(a + -10) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(a + -10) equal to 7.810249676 and -7.810249676.

Subproblem 1

a + -10 = 7.810249676 Simplifying a + -10 = 7.810249676 Reorder the terms: -10 + a = 7.810249676 Solving -10 + a = 7.810249676 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 7.810249676 + 10 Combine like terms: -10 + 10 = 0 0 + a = 7.810249676 + 10 a = 7.810249676 + 10 Combine like terms: 7.810249676 + 10 = 17.810249676 a = 17.810249676 Simplifying a = 17.810249676

Subproblem 2

a + -10 = -7.810249676 Simplifying a + -10 = -7.810249676 Reorder the terms: -10 + a = -7.810249676 Solving -10 + a = -7.810249676 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -7.810249676 + 10 Combine like terms: -10 + 10 = 0 0 + a = -7.810249676 + 10 a = -7.810249676 + 10 Combine like terms: -7.810249676 + 10 = 2.189750324 a = 2.189750324 Simplifying a = 2.189750324

Solution

The solution to the problem is based on the solutions from the subproblems. a = {17.810249676, 2.189750324}

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