200+5q+2q^2=5+4q

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Solution for 200+5q+2q^2=5+4q equation:


Simplifying
200 + 5q + 2q2 = 5 + 4q

Solving
200 + 5q + 2q2 = 5 + 4q

Solving for variable 'q'.

Reorder the terms:
200 + -5 + 5q + -4q + 2q2 = 5 + 4q + -5 + -4q

Combine like terms: 200 + -5 = 195
195 + 5q + -4q + 2q2 = 5 + 4q + -5 + -4q

Combine like terms: 5q + -4q = 1q
195 + 1q + 2q2 = 5 + 4q + -5 + -4q

Reorder the terms:
195 + 1q + 2q2 = 5 + -5 + 4q + -4q

Combine like terms: 5 + -5 = 0
195 + 1q + 2q2 = 0 + 4q + -4q
195 + 1q + 2q2 = 4q + -4q

Combine like terms: 4q + -4q = 0
195 + 1q + 2q2 = 0

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

Divide each side by '2'.
97.5 + 0.5q + q2 = 0

Move the constant term to the right:

Add '-97.5' to each side of the equation.
97.5 + 0.5q + -97.5 + q2 = 0 + -97.5

Reorder the terms:
97.5 + -97.5 + 0.5q + q2 = 0 + -97.5

Combine like terms: 97.5 + -97.5 = 0.0
0.0 + 0.5q + q2 = 0 + -97.5
0.5q + q2 = 0 + -97.5

Combine like terms: 0 + -97.5 = -97.5
0.5q + q2 = -97.5

The q term is 0.5q.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5q + 0.0625 + q2 = -97.5 + 0.0625

Reorder the terms:
0.0625 + 0.5q + q2 = -97.5 + 0.0625

Combine like terms: -97.5 + 0.0625 = -97.4375
0.0625 + 0.5q + q2 = -97.4375

Factor a perfect square on the left side:
(q + 0.25)(q + 0.25) = -97.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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