Answer :
We start with the equation:
[tex]$$
2z^2 - 3 = 197.
$$[/tex]
Step 1. Add [tex]$3$[/tex] to both sides to isolate the quadratic term:
[tex]$$
2z^2 = 197 + 3 = 200.
$$[/tex]
Step 2. Divide both sides by [tex]$2$[/tex] to solve for [tex]$z^2$[/tex]:
[tex]$$
z^2 = \frac{200}{2} = 100.
$$[/tex]
Step 3. Take the square root of both sides, remembering that both positive and negative roots are possible:
[tex]$$
z = \sqrt{100} = 10 \quad \text{or} \quad z = -\sqrt{100} = -10.
$$[/tex]
Thus, the solutions to the equation are:
[tex]$$
z = 10 \quad \text{or} \quad z = -10.
$$[/tex]
[tex]$$
2z^2 - 3 = 197.
$$[/tex]
Step 1. Add [tex]$3$[/tex] to both sides to isolate the quadratic term:
[tex]$$
2z^2 = 197 + 3 = 200.
$$[/tex]
Step 2. Divide both sides by [tex]$2$[/tex] to solve for [tex]$z^2$[/tex]:
[tex]$$
z^2 = \frac{200}{2} = 100.
$$[/tex]
Step 3. Take the square root of both sides, remembering that both positive and negative roots are possible:
[tex]$$
z = \sqrt{100} = 10 \quad \text{or} \quad z = -\sqrt{100} = -10.
$$[/tex]
Thus, the solutions to the equation are:
[tex]$$
z = 10 \quad \text{or} \quad z = -10.
$$[/tex]
