a^2+6a-22=0

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Solution for a^2+6a-22=0 equation:


Simplifying
a2 + 6a + -22 = 0

Reorder the terms:
-22 + 6a + a2 = 0

Solving
-22 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 6a + 22 + a2 = 0 + 22

Reorder the terms:
-22 + 22 + 6a + a2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 6a + a2 = 0 + 22
6a + a2 = 0 + 22

Combine like terms: 0 + 22 = 22
6a + a2 = 22

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 22 + 9

Reorder the terms:
9 + 6a + a2 = 22 + 9

Combine like terms: 22 + 9 = 31
9 + 6a + a2 = 31

Factor a perfect square on the left side:
(a + 3)(a + 3) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(a + 3) equal to 5.567764363 and -5.567764363.

Subproblem 1

a + 3 = 5.567764363 Simplifying a + 3 = 5.567764363 Reorder the terms: 3 + a = 5.567764363 Solving 3 + a = 5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 5.567764363 + -3 Combine like terms: 3 + -3 = 0 0 + a = 5.567764363 + -3 a = 5.567764363 + -3 Combine like terms: 5.567764363 + -3 = 2.567764363 a = 2.567764363 Simplifying a = 2.567764363

Subproblem 2

a + 3 = -5.567764363 Simplifying a + 3 = -5.567764363 Reorder the terms: 3 + a = -5.567764363 Solving 3 + a = -5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -5.567764363 + -3 Combine like terms: 3 + -3 = 0 0 + a = -5.567764363 + -3 a = -5.567764363 + -3 Combine like terms: -5.567764363 + -3 = -8.567764363 a = -8.567764363 Simplifying a = -8.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.567764363, -8.567764363}

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