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

Jun 3, 2016

$v = \sqrt{34} + 2 = 7.831 \text{ } \mathmr{and} v = - \sqrt{34} + 2 = - 3.831$

Explanation:

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

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

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

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

${\left(v - 2\right)}^{2} = 34$

Step 4. Find the square root of both sides.

$v - 2 = \pm \sqrt{34} \text{ } \Rightarrow v = \pm \sqrt{34} + 2$

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

$v = \sqrt{34} + 2 = 7.831 \text{ } \mathmr{and} v = - \sqrt{34} + 2 = - 3.831$