Q^2-30Q-1755=0

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Solution for Q^2-30Q-1755=0 equation: 


Simplifying
Q2 + -30Q + -1755 = 0

Reorder the terms:
-1755 + -30Q + Q2 = 0

Solving
-1755 + -30Q + Q2 = 0

Solving for variable 'Q'.

Begin completing the square.

Move the constant term to the right:

Add '1755' to each side of the equation.
-1755 + -30Q + 1755 + Q2 = 0 + 1755

Reorder the terms:
-1755 + 1755 + -30Q + Q2 = 0 + 1755

Combine like terms: -1755 + 1755 = 0
0 + -30Q + Q2 = 0 + 1755
-30Q + Q2 = 0 + 1755

Combine like terms: 0 + 1755 = 1755
-30Q + Q2 = 1755

The Q term is -30Q.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30Q + 225 + Q2 = 1755 + 225

Reorder the terms:
225 + -30Q + Q2 = 1755 + 225

Combine like terms: 1755 + 225 = 1980
225 + -30Q + Q2 = 1980

Factor a perfect square on the left side:
(Q + -15)(Q + -15) = 1980

Calculate the square root of the right side: 44.497190923

Break this problem into two subproblems by setting 
(Q + -15) equal to 44.497190923 and -44.497190923.


Subproblem 1
Q + -15 = 44.497190923

Simplifying
Q + -15 = 44.497190923

Reorder the terms:
-15 + Q = 44.497190923

Solving
-15 + Q = 44.497190923

Solving for variable 'Q'.

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

Add '15' to each side of the equation.
-15 + 15 + Q = 44.497190923 + 15

Combine like terms: -15 + 15 = 0
0 + Q = 44.497190923 + 15
Q = 44.497190923 + 15

Combine like terms: 44.497190923 + 15 = 59.497190923
Q = 59.497190923

Simplifying
Q = 59.497190923


Subproblem 2
Q + -15 = -44.497190923

Simplifying
Q + -15 = -44.497190923

Reorder the terms:
-15 + Q = -44.497190923

Solving
-15 + Q = -44.497190923

Solving for variable 'Q'.

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

Add '15' to each side of the equation.
-15 + 15 + Q = -44.497190923 + 15

Combine like terms: -15 + 15 = 0
0 + Q = -44.497190923 + 15
Q = -44.497190923 + 15

Combine like terms: -44.497190923 + 15 = -29.497190923
Q = -29.497190923

Simplifying
Q = -29.497190923


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {59.497190923, -29.497190923}

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