-7736q*65555q-772644*(368q+56)=628q-(6789976677q-777762)*9

Solution for -7736q*65555q-772644*(368q+56)=628q-(6789976677q-777762)*9 equation:

Simplifying
-7736q * 65555q + -772644(368q + 56) = 628q + -1(6789976677q + -777762) * 9

Reorder the terms for easier multiplication:
-7736 * 65555q * q + -772644(368q + 56) = 628q + -1(6789976677q + -777762) * 9

Multiply -7736 * 65555
-507133480q * q + -772644(368q + 56) = 628q + -1(6789976677q + -777762) * 9

Multiply q * q
-507133480q2 + -772644(368q + 56) = 628q + -1(6789976677q + -777762) * 9

Reorder the terms:
-507133480q2 + -772644(56 + 368q) = 628q + -1(6789976677q + -777762) * 9
-507133480q2 + (56 * -772644 + 368q * -772644) = 628q + -1(6789976677q + -777762) * 9
-507133480q2 + (-43268064 + -284332992q) = 628q + -1(6789976677q + -777762) * 9

Reorder the terms:
-43268064 + -284332992q + -507133480q2 = 628q + -1(6789976677q + -777762) * 9

Reorder the terms:
-43268064 + -284332992q + -507133480q2 = 628q + -1(-777762 + 6789976677q) * 9

Reorder the terms for easier multiplication:
-43268064 + -284332992q + -507133480q2 = 628q + -1 * 9(-777762 + 6789976677q)

Multiply -1 * 9
-43268064 + -284332992q + -507133480q2 = 628q + -9(-777762 + 6789976677q)
-43268064 + -284332992q + -507133480q2 = 628q + (-777762 * -9 + 6789976677q * -9)
-43268064 + -284332992q + -507133480q2 = 628q + (6999858 + -61109790090q)

Reorder the terms:
-43268064 + -284332992q + -507133480q2 = 6999858 + 628q + -61109790090q

Combine like terms: 628q + -61109790090q = -61109789462q
-43268064 + -284332992q + -507133480q2 = 6999858 + -61109789462q

Solving
-43268064 + -284332992q + -507133480q2 = 6999858 + -61109789462q

Solving for variable 'q'.

Reorder the terms:
-43268064 + -6999858 + -284332992q + 61109789462q + -507133480q2 = 6999858 + -61109789462q + -6999858 + 61109789462q

Combine like terms: -43268064 + -6999858 = -50267922
-50267922 + -284332992q + 61109789462q + -507133480q2 = 6999858 + -61109789462q + -6999858 + 61109789462q

Combine like terms: -284332992q + 61109789462q = 60825456470q
-50267922 + 60825456470q + -507133480q2 = 6999858 + -61109789462q + -6999858 + 61109789462q

Reorder the terms:
-50267922 + 60825456470q + -507133480q2 = 6999858 + -6999858 + -61109789462q + 61109789462q

Combine like terms: 6999858 + -6999858 = 0
-50267922 + 60825456470q + -507133480q2 = 0 + -61109789462q + 61109789462q
-50267922 + 60825456470q + -507133480q2 = -61109789462q + 61109789462q

Combine like terms: -61109789462q + 61109789462q = 0
-50267922 + 60825456470q + -507133480q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25133961 + 30412728240q + -253566740q2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25133961 + 30412728240q + -253566740q2)' equal to zero and attempt to solve:

Simplifying
-25133961 + 30412728240q + -253566740q2 = 0

Solving
-25133961 + 30412728240q + -253566740q2 = 0

Begin completing the square.  Divide all terms by
-253566740 the coefficient of the squared term: 

Divide each side by '-253566740'.
0.09912167897 + -119.9397375q + q2 = 0.0

Move the constant term to the right:

Add '-0.09912167897' to each side of the equation.
0.09912167897 + -119.9397375q + -0.09912167897 + q2 = 0.0 + -0.09912167897

Reorder the terms:
0.09912167897 + -0.09912167897 + -119.9397375q + q2 = 0.0 + -0.09912167897

Combine like terms: 0.09912167897 + -0.09912167897 = 0.00000000000
0.00000000000 + -119.9397375q + q2 = 0.0 + -0.09912167897
-119.9397375q + q2 = 0.0 + -0.09912167897

Combine like terms: 0.0 + -0.09912167897 = -0.09912167897
-119.9397375q + q2 = -0.09912167897

The q term is -119.9397375q.  Take half its coefficient (-59.96986875).
Square it (3596.385158) and add it to both sides.

Add '3596.385158' to each side of the equation.
-119.9397375q + 3596.385158 + q2 = -0.09912167897 + 3596.385158

Reorder the terms:
3596.385158 + -119.9397375q + q2 = -0.09912167897 + 3596.385158

Combine like terms: -0.09912167897 + 3596.385158 = 3596.28603632103
3596.385158 + -119.9397375q + q2 = 3596.28603632103

Factor a perfect square on the left side:
(q + -59.96986875)(q + -59.96986875) = 3596.28603632103

Calculate the square root of the right side: 59.969042316

Break this problem into two subproblems by setting 
(q + -59.96986875) equal to 59.969042316 and -59.969042316.

Subproblem 1
q + -59.96986875 = 59.969042316

Simplifying
q + -59.96986875 = 59.969042316

Reorder the terms:
-59.96986875 + q = 59.969042316

Solving
-59.96986875 + q = 59.969042316

Solving for variable 'q'.

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

Add '59.96986875' to each side of the equation.
-59.96986875 + 59.96986875 + q = 59.969042316 + 59.96986875

Combine like terms: -59.96986875 + 59.96986875 = 0.00000000
0.00000000 + q = 59.969042316 + 59.96986875
q = 59.969042316 + 59.96986875

Combine like terms: 59.969042316 + 59.96986875 = 119.938911066
q = 119.938911066

Simplifying
q = 119.938911066

Subproblem 2
q + -59.96986875 = -59.969042316

Simplifying
q + -59.96986875 = -59.969042316

Reorder the terms:
-59.96986875 + q = -59.969042316

Solving
-59.96986875 + q = -59.969042316

Solving for variable 'q'.

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

Add '59.96986875' to each side of the equation.
-59.96986875 + 59.96986875 + q = -59.969042316 + 59.96986875

Combine like terms: -59.96986875 + 59.96986875 = 0.00000000
0.00000000 + q = -59.969042316 + 59.96986875
q = -59.969042316 + 59.96986875

Combine like terms: -59.969042316 + 59.96986875 = 0.000826434
q = 0.000826434

Simplifying
q = 0.000826434

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {119.938911066, 0.000826434}
Solution
q = {119.938911066, 0.000826434}