a^2+3a-42=0

Solution for a^2+3a-42=0 equation:

Simplifying
a2 + 3a + -42 = 0

Reorder the terms:
-42 + 3a + a2 = 0

Solving
-42 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 3a + 42 + a2 = 0 + 42

Reorder the terms:
-42 + 42 + 3a + a2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 3a + a2 = 0 + 42
3a + a2 = 0 + 42

Combine like terms: 0 + 42 = 42
3a + a2 = 42

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 = 42 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 42 + 2.25

Combine like terms: 42 + 2.25 = 44.25
2.25 + 3a + a2 = 44.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(a + 1.5) equal to 6.652067348 and -6.652067348.

Subproblem 1
a + 1.5 = 6.652067348

Simplifying
a + 1.5 = 6.652067348

Reorder the terms:
1.5 + a = 6.652067348

Solving
1.5 + a = 6.652067348

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 = 6.652067348 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 6.652067348 + -1.5
a = 6.652067348 + -1.5

Combine like terms: 6.652067348 + -1.5 = 5.152067348
a = 5.152067348

Simplifying
a = 5.152067348

Subproblem 2
a + 1.5 = -6.652067348

Simplifying
a + 1.5 = -6.652067348

Reorder the terms:
1.5 + a = -6.652067348

Solving
1.5 + a = -6.652067348

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 = -6.652067348 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -6.652067348 + -1.5
a = -6.652067348 + -1.5

Combine like terms: -6.652067348 + -1.5 = -8.152067348
a = -8.152067348

Simplifying
a = -8.152067348

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.152067348, -8.152067348}