a^2+11a-68=0

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Solution for a^2+11a-68=0 equation: 


Simplifying
a2 + 11a + -68 = 0

Reorder the terms:
-68 + 11a + a2 = 0

Solving
-68 + 11a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 11a + 68 + a2 = 0 + 68

Reorder the terms:
-68 + 68 + 11a + a2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 11a + a2 = 0 + 68
11a + a2 = 0 + 68

Combine like terms: 0 + 68 = 68
11a + a2 = 68

The a term is 11a.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11a + 30.25 + a2 = 68 + 30.25

Reorder the terms:
30.25 + 11a + a2 = 68 + 30.25

Combine like terms: 68 + 30.25 = 98.25
30.25 + 11a + a2 = 98.25

Factor a perfect square on the left side:
(a + 5.5)(a + 5.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(a + 5.5) equal to 9.912113801 and -9.912113801.


Subproblem 1
a + 5.5 = 9.912113801

Simplifying
a + 5.5 = 9.912113801

Reorder the terms:
5.5 + a = 9.912113801

Solving
5.5 + a = 9.912113801

Solving for variable 'a'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + a = 9.912113801 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + a = 9.912113801 + -5.5
a = 9.912113801 + -5.5

Combine like terms: 9.912113801 + -5.5 = 4.412113801
a = 4.412113801

Simplifying
a = 4.412113801


Subproblem 2
a + 5.5 = -9.912113801

Simplifying
a + 5.5 = -9.912113801

Reorder the terms:
5.5 + a = -9.912113801

Solving
5.5 + a = -9.912113801

Solving for variable 'a'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + a = -9.912113801 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + a = -9.912113801 + -5.5
a = -9.912113801 + -5.5

Combine like terms: -9.912113801 + -5.5 = -15.412113801
a = -15.412113801

Simplifying
a = -15.412113801


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.412113801, -15.412113801}

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