x^2+18x+c=25+c

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Solution for x^2+18x+c=25+c equation: 


Simplifying
x2 + 18x + c = 25 + c

Reorder the terms:
c + 18x + x2 = 25 + c

Add '-1c' to each side of the equation.
c + 18x + -1c + x2 = 25 + c + -1c

Reorder the terms:
c + -1c + 18x + x2 = 25 + c + -1c

Combine like terms: c + -1c = 0
0 + 18x + x2 = 25 + c + -1c
18x + x2 = 25 + c + -1c

Combine like terms: c + -1c = 0
18x + x2 = 25 + 0
18x + x2 = 25

Solving
18x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 18x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 18x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 18x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 18x + x2 = 0 + 25
18x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
18x + x2 = 25

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

Add '81' to each side of the equation.
18x + 81 + x2 = 25 + 81

Reorder the terms:
81 + 18x + x2 = 25 + 81

Combine like terms: 25 + 81 = 106
81 + 18x + x2 = 106

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

Calculate the square root of the right side: 10.295630141

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


Subproblem 1
x + 9 = 10.295630141

Simplifying
x + 9 = 10.295630141

Reorder the terms:
9 + x = 10.295630141

Solving
9 + x = 10.295630141

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 1.295630141


Subproblem 2
x + 9 = -10.295630141

Simplifying
x + 9 = -10.295630141

Reorder the terms:
9 + x = -10.295630141

Solving
9 + x = -10.295630141

Solving for variable 'x'.

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

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

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

Combine like terms: -10.295630141 + -9 = -19.295630141
x = -19.295630141

Simplifying
x = -19.295630141


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

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