a^2-4a-41=0

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Solution for a^2-4a-41=0 equation:


Simplifying
a2 + -4a + -41 = 0

Reorder the terms:
-41 + -4a + a2 = 0

Solving
-41 + -4a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -4a + 41 + a2 = 0 + 41

Reorder the terms:
-41 + 41 + -4a + a2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -4a + a2 = 0 + 41
-4a + a2 = 0 + 41

Combine like terms: 0 + 41 = 41
-4a + a2 = 41

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = 41 + 4

Reorder the terms:
4 + -4a + a2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + -4a + a2 = 45

Factor a perfect square on the left side:
(a + -2)(a + -2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(a + -2) equal to 6.708203933 and -6.708203933.

Subproblem 1

a + -2 = 6.708203933 Simplifying a + -2 = 6.708203933 Reorder the terms: -2 + a = 6.708203933 Solving -2 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + a = 6.708203933 + 2 a = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 a = 8.708203933 Simplifying a = 8.708203933

Subproblem 2

a + -2 = -6.708203933 Simplifying a + -2 = -6.708203933 Reorder the terms: -2 + a = -6.708203933 Solving -2 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + a = -6.708203933 + 2 a = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 a = -4.708203933 Simplifying a = -4.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.708203933, -4.708203933}

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