Let's solve the equation [tex]\( 25b^2 - 64 = 0 \)[/tex] step-by-step.
1. Isolate the quadratic term: First, we need to express the equation such that we can solve for [tex]\( b \)[/tex]. Start by moving 64 to the right side:
[tex]\[
25b^2 - 64 + 64 = 64
\][/tex]
[tex]\[
25b^2 = 64
\][/tex]
2. Solve for [tex]\( b^2 \)[/tex]: Next, divide both sides by 25 to isolate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = \frac{64}{25}
\][/tex]
3. Take the square root of both sides: We now take the square root of both sides to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \pm \sqrt{\frac{64}{25}}
\][/tex]
[tex]\[
b = \pm \frac{\sqrt{64}}{\sqrt{25}}
\][/tex]
[tex]\[
b = \pm \frac{8}{5}
\][/tex]
Therefore, the solutions to the equation [tex]\( 25b^2 - 64 = 0 \)[/tex] are:
[tex]\[
b = \frac{8}{5} \quad \text{and} \quad b = -\frac{8}{5}
\][/tex]
Thus, the correct answer is:
[tex]\[
\frac{8}{5}, -\frac{8}{5}
\][/tex]
