# How do you solve the quadratic 7k^2+7=-140 using any method?

Sep 4, 2016

$k = \pm i \sqrt{21}$

#### Explanation:

Begin by isolating ${k}^{2}$

$7 {k}^{2} = - 140 - 7 = - 147$

$\Rightarrow {k}^{2} = \frac{- 147}{7} = - 21$

now take the $\textcolor{b l u e}{\text{square root}}$ of both sides

$\Rightarrow \sqrt{{k}^{2}} = \pm \sqrt{- 21} \Rightarrow k = \pm \sqrt{- 21}$

Now $\sqrt{- 21} = \sqrt{- 1 \times 21} = \sqrt{- 1} \times \sqrt{21} = i \sqrt{21}$

$\Rightarrow k = \pm i \sqrt{21}$