Checkpoint: The Square Root Property to Solve Solution

Checkpoint: The Square Root Property to Solve Solution

Solve.

${(3 x - 1)}^{2} = - 12$

$\begin{array}{rcl} \sqrt{{(3 x - 1)}^{2}} & = & \pm \sqrt{- 12} \\ 3 x - 1 & = & \pm 2 i \sqrt{3} \\ 3 x & = & 1 \pm 2 i \sqrt{3} \end{array}$

$\begin{array}{rcl} x & = & \frac{1 \pm 2 i \sqrt{3}}{3} \end{array}$

Note

Q: What needs to be factored out first when the radicand is a negative number?

A: –1 

Q: How many solutions will this equation have? Explain.

A: There will be 2 solutions because the degree is two.