2a^2-a-11=0

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


Simplifying
2a2 + -1a + -11 = 0

Reorder the terms:
-11 + -1a + 2a2 = 0

Solving
-11 + -1a + 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'.
-5.5 + -0.5a + a2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -0.5a + 5.5 + a2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -0.5a + a2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -0.5a + a2 = 0 + 5.5
-0.5a + a2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-0.5a + a2 = 5.5

The a term is -0.5a.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a + 0.0625 + a2 = 5.5 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = 5.5 + 0.0625

Combine like terms: 5.5 + 0.0625 = 5.5625
0.0625 + -0.5a + a2 = 5.5625

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(a + -0.25) equal to 2.358495283 and -2.358495283.

Subproblem 1

a + -0.25 = 2.358495283 Simplifying a + -0.25 = 2.358495283 Reorder the terms: -0.25 + a = 2.358495283 Solving -0.25 + a = 2.358495283 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 2.358495283 + 0.25 a = 2.358495283 + 0.25 Combine like terms: 2.358495283 + 0.25 = 2.608495283 a = 2.608495283 Simplifying a = 2.608495283

Subproblem 2

a + -0.25 = -2.358495283 Simplifying a + -0.25 = -2.358495283 Reorder the terms: -0.25 + a = -2.358495283 Solving -0.25 + a = -2.358495283 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -2.358495283 + 0.25 a = -2.358495283 + 0.25 Combine like terms: -2.358495283 + 0.25 = -2.108495283 a = -2.108495283 Simplifying a = -2.108495283

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.608495283, -2.108495283}

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