-2q^2+7q*11=1

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Solution for -2q^2+7q*11=1 equation: 


Simplifying
-2q2 + 7q * 11 = 1

Reorder the terms for easier multiplication:
-2q2 + 7 * 11q = 1

Multiply 7 * 11
-2q2 + 77q = 1

Reorder the terms:
77q + -2q2 = 1

Solving
77q + -2q2 = 1

Solving for variable 'q'.

Reorder the terms:
-1 + 77q + -2q2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 77q + -2q2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -38.5q + q2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -38.5q + -0.5 + q2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -38.5q + q2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -38.5q + q2 = 0 + -0.5
-38.5q + q2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-38.5q + q2 = -0.5

The q term is -38.5q.  Take half its coefficient (-19.25).
Square it (370.5625) and add it to both sides.

Add '370.5625' to each side of the equation.
-38.5q + 370.5625 + q2 = -0.5 + 370.5625

Reorder the terms:
370.5625 + -38.5q + q2 = -0.5 + 370.5625

Combine like terms: -0.5 + 370.5625 = 370.0625
370.5625 + -38.5q + q2 = 370.0625

Factor a perfect square on the left side:
(q + -19.25)(q + -19.25) = 370.0625

Calculate the square root of the right side: 19.237008603

Break this problem into two subproblems by setting 
(q + -19.25) equal to 19.237008603 and -19.237008603.


Subproblem 1
q + -19.25 = 19.237008603

Simplifying
q + -19.25 = 19.237008603

Reorder the terms:
-19.25 + q = 19.237008603

Solving
-19.25 + q = 19.237008603

Solving for variable 'q'.

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

Add '19.25' to each side of the equation.
-19.25 + 19.25 + q = 19.237008603 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + q = 19.237008603 + 19.25
q = 19.237008603 + 19.25

Combine like terms: 19.237008603 + 19.25 = 38.487008603
q = 38.487008603

Simplifying
q = 38.487008603


Subproblem 2
q + -19.25 = -19.237008603

Simplifying
q + -19.25 = -19.237008603

Reorder the terms:
-19.25 + q = -19.237008603

Solving
-19.25 + q = -19.237008603

Solving for variable 'q'.

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

Add '19.25' to each side of the equation.
-19.25 + 19.25 + q = -19.237008603 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + q = -19.237008603 + 19.25
q = -19.237008603 + 19.25

Combine like terms: -19.237008603 + 19.25 = 0.012991397
q = 0.012991397

Simplifying
q = 0.012991397


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {38.487008603, 0.012991397}

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