a^2+3a-50=0

Solution for a^2+3a-50=0 equation:

Simplifying
a2 + 3a + -50 = 0

Reorder the terms:
-50 + 3a + a2 = 0

Solving
-50 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 3a + 50 + a2 = 0 + 50

Reorder the terms:
-50 + 50 + 3a + a2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 3a + a2 = 0 + 50
3a + a2 = 0 + 50

Combine like terms: 0 + 50 = 50
3a + a2 = 50

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 = 50 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 50 + 2.25

Combine like terms: 50 + 2.25 = 52.25
2.25 + 3a + a2 = 52.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(a + 1.5) equal to 7.228416147 and -7.228416147.

Subproblem 1
a + 1.5 = 7.228416147

Simplifying
a + 1.5 = 7.228416147

Reorder the terms:
1.5 + a = 7.228416147

Solving
1.5 + a = 7.228416147

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 = 7.228416147 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 7.228416147 + -1.5
a = 7.228416147 + -1.5

Combine like terms: 7.228416147 + -1.5 = 5.728416147
a = 5.728416147

Simplifying
a = 5.728416147

Subproblem 2
a + 1.5 = -7.228416147

Simplifying
a + 1.5 = -7.228416147

Reorder the terms:
1.5 + a = -7.228416147

Solving
1.5 + a = -7.228416147

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 = -7.228416147 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -7.228416147 + -1.5
a = -7.228416147 + -1.5

Combine like terms: -7.228416147 + -1.5 = -8.728416147
a = -8.728416147

Simplifying
a = -8.728416147

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.728416147, -8.728416147}