q^2+18q=25

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Solution for q^2+18q=25 equation: 


Simplifying
q2 + 18q = 25

Reorder the terms:
18q + q2 = 25

Solving
18q + q2 = 25

Solving for variable 'q'.

Reorder the terms:
-25 + 18q + q2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 18q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 18q + 25 + q2 = 0 + 25

Reorder the terms:
-25 + 25 + 18q + q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 18q + q2 = 0 + 25
18q + q2 = 0 + 25

Combine like terms: 0 + 25 = 25
18q + q2 = 25

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

Add '81' to each side of the equation.
18q + 81 + q2 = 25 + 81

Reorder the terms:
81 + 18q + q2 = 25 + 81

Combine like terms: 25 + 81 = 106
81 + 18q + q2 = 106

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

Calculate the square root of the right side: 10.295630141

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


Subproblem 1
q + 9 = 10.295630141

Simplifying
q + 9 = 10.295630141

Reorder the terms:
9 + q = 10.295630141

Solving
9 + q = 10.295630141

Solving for variable 'q'.

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

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

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

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

Simplifying
q = 1.295630141


Subproblem 2
q + 9 = -10.295630141

Simplifying
q + 9 = -10.295630141

Reorder the terms:
9 + q = -10.295630141

Solving
9 + q = -10.295630141

Solving for variable 'q'.

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

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

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

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

Simplifying
q = -19.295630141


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

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