Answer :
We start with the equation
[tex]$$
8b^2 - 7 = 193.
$$[/tex]
Step 1: Isolate the term with [tex]\(b^2\)[/tex].
Add 7 to both sides:
[tex]$$
8b^2 - 7 + 7 = 193 + 7,
$$[/tex]
which simplifies to
[tex]$$
8b^2 = 200.
$$[/tex]
Step 2: Solve for [tex]\(b^2\)[/tex].
Divide both sides by 8:
[tex]$$
b^2 = \frac{200}{8} = 25.
$$[/tex]
Step 3: Solve for [tex]\(b\)[/tex].
Taking the square root of both sides gives:
[tex]$$
b = \pm \sqrt{25} = \pm 5.
$$[/tex]
Conclusion:
The solutions to the equation are
[tex]$$
b = 5 \quad \text{and} \quad b = -5.
$$[/tex]
[tex]$$
8b^2 - 7 = 193.
$$[/tex]
Step 1: Isolate the term with [tex]\(b^2\)[/tex].
Add 7 to both sides:
[tex]$$
8b^2 - 7 + 7 = 193 + 7,
$$[/tex]
which simplifies to
[tex]$$
8b^2 = 200.
$$[/tex]
Step 2: Solve for [tex]\(b^2\)[/tex].
Divide both sides by 8:
[tex]$$
b^2 = \frac{200}{8} = 25.
$$[/tex]
Step 3: Solve for [tex]\(b\)[/tex].
Taking the square root of both sides gives:
[tex]$$
b = \pm \sqrt{25} = \pm 5.
$$[/tex]
Conclusion:
The solutions to the equation are
[tex]$$
b = 5 \quad \text{and} \quad b = -5.
$$[/tex]
