29=a^2+3a-1

Solution for 29=a^2+3a-1 equation:

Simplifying
29 = a2 + 3a + -1

Reorder the terms:
29 = -1 + 3a + a2

Solving
29 = -1 + 3a + a2

Solving for variable 'a'.

Combine like terms: 29 + 1 = 30
30 + -3a + -1a2 = -1 + 3a + a2 + 1 + -3a + -1a2

Reorder the terms:
30 + -3a + -1a2 = -1 + 1 + 3a + -3a + a2 + -1a2

Combine like terms: -1 + 1 = 0
30 + -3a + -1a2 = 0 + 3a + -3a + a2 + -1a2
30 + -3a + -1a2 = 3a + -3a + a2 + -1a2

Combine like terms: 3a + -3a = 0
30 + -3a + -1a2 = 0 + a2 + -1a2
30 + -3a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
30 + -3a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + 3a + a2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3a + 30 + a2 = 0 + 30

Reorder the terms:
-30 + 30 + 3a + a2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3a + a2 = 0 + 30
3a + a2 = 0 + 30

Combine like terms: 0 + 30 = 30
3a + a2 = 30

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 30 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3a + a2 = 32.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(a + 1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
a + 1.5 = 5.678908346

Simplifying
a + 1.5 = 5.678908346

Reorder the terms:
1.5 + a = 5.678908346

Solving
1.5 + a = 5.678908346

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 5.678908346 + -1.5
a = 5.678908346 + -1.5

Combine like terms: 5.678908346 + -1.5 = 4.178908346
a = 4.178908346

Simplifying
a = 4.178908346

Subproblem 2
a + 1.5 = -5.678908346

Simplifying
a + 1.5 = -5.678908346

Reorder the terms:
1.5 + a = -5.678908346

Solving
1.5 + a = -5.678908346

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -5.678908346 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -5.678908346 + -1.5
a = -5.678908346 + -1.5

Combine like terms: -5.678908346 + -1.5 = -7.178908346
a = -7.178908346

Simplifying
a = -7.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.178908346, -7.178908346}