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

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Answer 1 · 2016-06-03T23:11:06

$v = \sqrt{34} + 2 = 7.831 or v = - \sqrt{34} + 2 = - 3.831$ $v = sqrt34 +2 = 7.831 " " or v =-sqrt34 +2 = -3.831$

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

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

$v^{2} - 4 v + 4 = 30 + 4$ $v^2 - 4v + 4 = 30 + 4$

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

${(v - 2)}^{2} = 34$ $(v - 2)^2 = 34$

Step 4. Find the square root of both sides.

$v - 2 = \pm \sqrt{34} \Rightarrow v = \pm \sqrt{34} + 2$ $v - 2 = +-sqrt34 " " rArr v= +-sqrt34 +2$

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

$v = \sqrt{34} + 2 = 7.831 or v = - \sqrt{34} + 2 = - 3.831$ $v = sqrt34 +2 = 7.831 " " or v =-sqrt34 +2 = -3.831$

How do you solve v2−4v−30=0v^2 - 4v - 30 = 0 by completing the square?