a^2+19a-57=0

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Solution for a^2+19a-57=0 equation:


Simplifying
a2 + 19a + -57 = 0

Reorder the terms:
-57 + 19a + a2 = 0

Solving
-57 + 19a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 19a + 57 + a2 = 0 + 57

Reorder the terms:
-57 + 57 + 19a + a2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 19a + a2 = 0 + 57
19a + a2 = 0 + 57

Combine like terms: 0 + 57 = 57
19a + a2 = 57

The a term is 19a.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19a + 90.25 + a2 = 57 + 90.25

Reorder the terms:
90.25 + 19a + a2 = 57 + 90.25

Combine like terms: 57 + 90.25 = 147.25
90.25 + 19a + a2 = 147.25

Factor a perfect square on the left side:
(a + 9.5)(a + 9.5) = 147.25

Calculate the square root of the right side: 12.1346611

Break this problem into two subproblems by setting 
(a + 9.5) equal to 12.1346611 and -12.1346611.


Subproblem 1
a + 9.5 = 12.1346611

Simplifying
a + 9.5 = 12.1346611

Reorder the terms:
9.5 + a = 12.1346611

Solving
9.5 + a = 12.1346611

Solving for variable 'a'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + a = 12.1346611 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + a = 12.1346611 + -9.5
a = 12.1346611 + -9.5

Combine like terms: 12.1346611 + -9.5 = 2.6346611
a = 2.6346611

Simplifying
a = 2.6346611


Subproblem 2
a + 9.5 = -12.1346611

Simplifying
a + 9.5 = -12.1346611

Reorder the terms:
9.5 + a = -12.1346611

Solving
9.5 + a = -12.1346611

Solving for variable 'a'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + a = -12.1346611 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + a = -12.1346611 + -9.5
a = -12.1346611 + -9.5

Combine like terms: -12.1346611 + -9.5 = -21.6346611
a = -21.6346611

Simplifying
a = -21.6346611


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.6346611, -21.6346611}

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