Question

What values of b satisfy 4(3b + 2)2 = 64?

Answer 1

Answer

b=\frac{2}{3} and b=-2

Step-by-step explanation:

Answer 2

Answer:

$b=\frac{2}{3}$ and $b=-2$

Step-by-step explanation:

Given:

$4(3b+2)^{2}=64$

In order to find the values of b, we need to solve the equation for b.

Divide both sides by 4.

This gives,

$4(3b+2)^{2}=64\\ \frac{4(3b+2)^{2}}{4}=\frac{64}{4}\\ (3b+2)^{2}=16$

Taking square root both sides, we get,

$\sqrt{(3b+2)^2}=\sqrt{16}\\3b+2=\pm 4\\3b=\pm 4-2\\b=\frac{-2\pm 4}{3}$

Now, $b=\frac{-2+4}{3}\textrm{ or } b=\frac{-2-4}{3}\\b=\frac{2}{3}\textrm{ or } b=\frac{-6}{3}\\b=\frac{2}{3}\textrm{ or } b=-2$