Question

solve the following equation using the square root property.
$2x^2 - 7 = -105$

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 7 to both sides:
$2x^2 - 7 + 7 = -105 + 7$
$2x^2 = -98$

Step2: Solve for $x^2$

Divide both sides by 2:
$\frac{2x^2}{2} = \frac{-98}{2}$
$x^2 = -49$

Step3: Apply square root property

Take square root of both sides, use $i=\sqrt{-1}$:
$x = \pm\sqrt{-49} = \pm\sqrt{49 \times (-1)} = \pm7i$

Answer:

$\{7i, -7i\}$