Question

Solve by completing the square.

$v^2-14v=-31$

Short answer

The solution is$v=\pm 3\sqrt{2}+7$.

Step-by-step solution

Step 1. Given information.

The given equation is$v^2-14v=-31$.

Step 2. Simplify the equation.

$\begin{array}{rcl}{v}^2-14v& =& -31\\ v^2-2·v·7& =& -31\\ v^2-2·v·7+49& =& -31+49\cdots \cdots \left(add49onbothsides\right)\\ v^2-2·v·7+7^2& =& 18\\ {\left(v-7\right)}^2& =& 18\\ v-7& =& \pm \sqrt{18}\\ v-7& =& \pm 3\sqrt{2}\\ v& =& \pm 3\sqrt{2}+7\end{array}$

Step 3. Simplified answer.

Hence, the required solution is$v=\pm 3\sqrt{2}+7$.