v^2-9=2v^2-7v+7

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Solution for v^2-9=2v^2-7v+7 equation: 


Simplifying
v2 + -9 = 2v2 + -7v + 7

Reorder the terms:
-9 + v2 = 2v2 + -7v + 7

Reorder the terms:
-9 + v2 = 7 + -7v + 2v2

Solving
-9 + v2 = 7 + -7v + 2v2

Solving for variable 'v'.

Reorder the terms:
-9 + -7 + 7v + v2 + -2v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Combine like terms: -9 + -7 = -16
-16 + 7v + v2 + -2v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-16 + 7v + -1v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Reorder the terms:
-16 + 7v + -1v2 = 7 + -7 + -7v + 7v + 2v2 + -2v2

Combine like terms: 7 + -7 = 0
-16 + 7v + -1v2 = 0 + -7v + 7v + 2v2 + -2v2
-16 + 7v + -1v2 = -7v + 7v + 2v2 + -2v2

Combine like terms: -7v + 7v = 0
-16 + 7v + -1v2 = 0 + 2v2 + -2v2
-16 + 7v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-16 + 7v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16 + -7v + v2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -7v + -16 + v2 = 0 + -16

Reorder the terms:
16 + -16 + -7v + v2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -7v + v2 = 0 + -16
-7v + v2 = 0 + -16

Combine like terms: 0 + -16 = -16
-7v + v2 = -16

The v term is -7v.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7v + 12.25 + v2 = -16 + 12.25

Reorder the terms:
12.25 + -7v + v2 = -16 + 12.25

Combine like terms: -16 + 12.25 = -3.75
12.25 + -7v + v2 = -3.75

Factor a perfect square on the left side:
(v + -3.5)(v + -3.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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