Question

Solve quadratic equation${\left(5c+1\right)}^2=-27$ using square root property

Short answer

The values of$c$are$\frac{-1-3\sqrt{3}\iota }{5}$and$\frac{-1+3\sqrt{3}\iota }{5}$

Step-by-step solution

Step 1. Given information 

The quadratic equation${\left(5c+1\right)}^2=-27$

Step 2. Use square root property 

$\Rightarrow 5c+1=\pm \sqrt{-27}$

$\Rightarrow 5c=-1\pm 3\sqrt{3}\iota$

$\Rightarrow c=\frac{-1\pm 3\sqrt{3}\iota }{5}$

localid="1645626198613" $\Rightarrow c=\frac{-1-3\sqrt{3}\iota }{5}$andlocalid="1645626208602" $c=\frac{-1+3\sqrt{3}\iota }{5}$