Question

solve the following equation using the square root property.
$3x^2 - 3 = -51$

the solution set is
(simplify your answer. express complex numbers in terms of $i$. use a comma to separate answers as needed.)

Explanation:

Step1: Isolate the $x^2$ term

Add 3 to both sides:
$3x^2 - 3 + 3 = -51 + 3$
$3x^2 = -48$

Step2: Solve for $x^2$

Divide by 3 on both sides:
$\frac{3x^2}{3} = \frac{-48}{3}$
$x^2 = -16$

Step3: Apply square root property

Take square root of both sides, recall $\sqrt{-1}=i$:
$x = \pm\sqrt{-16} = \pm\sqrt{16 \times (-1)} = \pm 4i$

Answer:

$\pm 4i$