a^2-2a-11=0

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Solution for a^2-2a-11=0 equation:


Simplifying
a2 + -2a + -11 = 0

Reorder the terms:
-11 + -2a + a2 = 0

Solving
-11 + -2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2a + 11 + a2 = 0 + 11

Reorder the terms:
-11 + 11 + -2a + a2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2a + a2 = 0 + 11
-2a + a2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2a + a2 = 11

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 11 + 1

Reorder the terms:
1 + -2a + a2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2a + a2 = 12

Factor a perfect square on the left side:
(a + -1)(a + -1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(a + -1) equal to 3.464101615 and -3.464101615.

Subproblem 1

a + -1 = 3.464101615 Simplifying a + -1 = 3.464101615 Reorder the terms: -1 + a = 3.464101615 Solving -1 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + a = 3.464101615 + 1 a = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 a = 4.464101615 Simplifying a = 4.464101615

Subproblem 2

a + -1 = -3.464101615 Simplifying a + -1 = -3.464101615 Reorder the terms: -1 + a = -3.464101615 Solving -1 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + a = -3.464101615 + 1 a = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 a = -2.464101615 Simplifying a = -2.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.464101615, -2.464101615}

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