a^2-18a-25=0

Solution for a^2-18a-25=0 equation:

Simplifying
a2 + -18a + -25 = 0

Reorder the terms:
-25 + -18a + a2 = 0

Solving
-25 + -18a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -18a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + -18a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -18a + a2 = 0 + 25
-18a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
-18a + a2 = 25

The a term is -18a.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18a + 81 + a2 = 25 + 81

Reorder the terms:
81 + -18a + a2 = 25 + 81

Combine like terms: 25 + 81 = 106
81 + -18a + a2 = 106

Factor a perfect square on the left side:
(a + -9)(a + -9) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(a + -9) equal to 10.295630141 and -10.295630141.

Subproblem 1
a + -9 = 10.295630141

Simplifying
a + -9 = 10.295630141

Reorder the terms:
-9 + a = 10.295630141

Solving
-9 + a = 10.295630141

Solving for variable 'a'.

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

Add '9' to each side of the equation.
-9 + 9 + a = 10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + a = 10.295630141 + 9
a = 10.295630141 + 9

Combine like terms: 10.295630141 + 9 = 19.295630141
a = 19.295630141

Simplifying
a = 19.295630141

Subproblem 2
a + -9 = -10.295630141

Simplifying
a + -9 = -10.295630141

Reorder the terms:
-9 + a = -10.295630141

Solving
-9 + a = -10.295630141

Solving for variable 'a'.

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

Add '9' to each side of the equation.
-9 + 9 + a = -10.295630141 + 9

Combine like terms: -9 + 9 = 0
0 + a = -10.295630141 + 9
a = -10.295630141 + 9

Combine like terms: -10.295630141 + 9 = -1.295630141
a = -1.295630141

Simplifying
a = -1.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {19.295630141, -1.295630141}