Q^2-16Q=275

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Solution for Q^2-16Q=275 equation: 


Simplifying
Q2 + -16Q = 275

Reorder the terms:
-16Q + Q2 = 275

Solving
-16Q + Q2 = 275

Solving for variable 'Q'.

Reorder the terms:
-275 + -16Q + Q2 = 275 + -275

Combine like terms: 275 + -275 = 0
-275 + -16Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + -16Q + 275 + Q2 = 0 + 275

Reorder the terms:
-275 + 275 + -16Q + Q2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + -16Q + Q2 = 0 + 275
-16Q + Q2 = 0 + 275

Combine like terms: 0 + 275 = 275
-16Q + Q2 = 275

The Q term is -16Q.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16Q + 64 + Q2 = 275 + 64

Reorder the terms:
64 + -16Q + Q2 = 275 + 64

Combine like terms: 275 + 64 = 339
64 + -16Q + Q2 = 339

Factor a perfect square on the left side:
(Q + -8)(Q + -8) = 339

Calculate the square root of the right side: 18.41195264

Break this problem into two subproblems by setting 
(Q + -8) equal to 18.41195264 and -18.41195264.


Subproblem 1
Q + -8 = 18.41195264

Simplifying
Q + -8 = 18.41195264

Reorder the terms:
-8 + Q = 18.41195264

Solving
-8 + Q = 18.41195264

Solving for variable 'Q'.

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

Add '8' to each side of the equation.
-8 + 8 + Q = 18.41195264 + 8

Combine like terms: -8 + 8 = 0
0 + Q = 18.41195264 + 8
Q = 18.41195264 + 8

Combine like terms: 18.41195264 + 8 = 26.41195264
Q = 26.41195264

Simplifying
Q = 26.41195264


Subproblem 2
Q + -8 = -18.41195264

Simplifying
Q + -8 = -18.41195264

Reorder the terms:
-8 + Q = -18.41195264

Solving
-8 + Q = -18.41195264

Solving for variable 'Q'.

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

Add '8' to each side of the equation.
-8 + 8 + Q = -18.41195264 + 8

Combine like terms: -8 + 8 = 0
0 + Q = -18.41195264 + 8
Q = -18.41195264 + 8

Combine like terms: -18.41195264 + 8 = -10.41195264
Q = -10.41195264

Simplifying
Q = -10.41195264


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {26.41195264, -10.41195264}

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