How do you solve #v^2 - 4v - 30 = 0# by completing the square?

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Answer 1 · 2016-06-03T23:11:06

#v = sqrt34 +2 = 7.831 " " or v =-sqrt34 +2 = -3.831#

Step 1. Move the constant to the other side.
#v^2 - 4v " " = 30#

Step 2: -4 is the coefficient of the x-term
Halve it and square it and add to both sides.

#v^2 - 4v + 4 = 30 + 4#

Step 3; The left side can be written as a binomial squared.

#(v - 2)^2 = 34#

Step 4. Find the square root of both sides.

#v - 2 = +-sqrt34 " " rArr v= +-sqrt34 +2#

Step 5. Do two calculations - once with the positive root and once with the negative root.

#v = sqrt34 +2 = 7.831 " " or v =-sqrt34 +2 = -3.831#