2a^2-a-22=0

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Solution for 2a^2-a-22=0 equation:


Simplifying
2a2 + -1a + -22 = 0

Reorder the terms:
-22 + -1a + 2a2 = 0

Solving
-22 + -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'.
-11 + -0.5a + a2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -0.5a + 11 + a2 = 0 + 11

Reorder the terms:
-11 + 11 + -0.5a + a2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -0.5a + a2 = 0 + 11
-0.5a + a2 = 0 + 11

Combine like terms: 0 + 11 = 11
-0.5a + a2 = 11

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 = 11 + 0.0625

Reorder the terms:
0.0625 + -0.5a + a2 = 11 + 0.0625

Combine like terms: 11 + 0.0625 = 11.0625
0.0625 + -0.5a + a2 = 11.0625

Factor a perfect square on the left side:
(a + -0.25)(a + -0.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(a + -0.25) equal to 3.326033674 and -3.326033674.

Subproblem 1

a + -0.25 = 3.326033674 Simplifying a + -0.25 = 3.326033674 Reorder the terms: -0.25 + a = 3.326033674 Solving -0.25 + a = 3.326033674 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 = 3.326033674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 3.326033674 + 0.25 a = 3.326033674 + 0.25 Combine like terms: 3.326033674 + 0.25 = 3.576033674 a = 3.576033674 Simplifying a = 3.576033674

Subproblem 2

a + -0.25 = -3.326033674 Simplifying a + -0.25 = -3.326033674 Reorder the terms: -0.25 + a = -3.326033674 Solving -0.25 + a = -3.326033674 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 = -3.326033674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -3.326033674 + 0.25 a = -3.326033674 + 0.25 Combine like terms: -3.326033674 + 0.25 = -3.076033674 a = -3.076033674 Simplifying a = -3.076033674

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.576033674, -3.076033674}

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