4a^2+8a-21=21

Solution for 4a^2+8a-21=21 equation:

Simplifying
4a2 + 8a + -21 = 21

Reorder the terms:
-21 + 8a + 4a2 = 21

Solving
-21 + 8a + 4a2 = 21

Solving for variable 'a'.

Reorder the terms:
-21 + -21 + 8a + 4a2 = 21 + -21

Combine like terms: -21 + -21 = -42
-42 + 8a + 4a2 = 21 + -21

Combine like terms: 21 + -21 = 0
-42 + 8a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 4a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 4a + 2a2)' equal to zero and attempt to solve:

Simplifying
-21 + 4a + 2a2 = 0

Solving
-21 + 4a + 2a2 = 0

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

Divide each side by '2'.
-10.5 + 2a + a2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 2a + 10.5 + a2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 2a + a2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 2a + a2 = 0 + 10.5
2a + a2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
2a + a2 = 10.5

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 = 10.5 + 1

Reorder the terms:
1 + 2a + a2 = 10.5 + 1

Combine like terms: 10.5 + 1 = 11.5
1 + 2a + a2 = 11.5

Factor a perfect square on the left side:
(a + 1)(a + 1) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(a + 1) equal to 3.391164992 and -3.391164992.

Subproblem 1
a + 1 = 3.391164992

Simplifying
a + 1 = 3.391164992

Reorder the terms:
1 + a = 3.391164992

Solving
1 + a = 3.391164992

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 = 3.391164992 + -1

Combine like terms: 1 + -1 = 0
0 + a = 3.391164992 + -1
a = 3.391164992 + -1

Combine like terms: 3.391164992 + -1 = 2.391164992
a = 2.391164992

Simplifying
a = 2.391164992

Subproblem 2
a + 1 = -3.391164992

Simplifying
a + 1 = -3.391164992

Reorder the terms:
1 + a = -3.391164992

Solving
1 + a = -3.391164992

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 = -3.391164992 + -1

Combine like terms: 1 + -1 = 0
0 + a = -3.391164992 + -1
a = -3.391164992 + -1

Combine like terms: -3.391164992 + -1 = -4.391164992
a = -4.391164992

Simplifying
a = -4.391164992

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.391164992, -4.391164992}
Solution
a = {2.391164992, -4.391164992}