Question

Solve the equation. = 12 = 752 – 385 b = and b =

Answer 1

$-42=7b^2-385$

To solve the equation for b:

1. Add 385 in both sides of the equation:

$\begin{gathered} -42+385=7b^2-385+385 \\ 343=7b^2 \end{gathered}$

2. Divide both sides of the equation into 7:

$\begin{gathered} \frac{343}{7}=\frac{7}{7}b^2 \\ \\ 49=b^2 \end{gathered}$

3. Find the square root of both terms:

$\begin{gathered} \sqrt[]{49}=\sqrt{b^2} \\ \sqrt[]{49}=b \end{gathered}$

4. In this case you can write the 49 under the root as:

$\begin{gathered} \sqrt[]{49}=\sqrt[]{(7)^2} \\ \sqrt[]{49}=\sqrt[]{(-7)^2} \\ \\ \sqrt[]{49}=\pm7 \end{gathered}$

Then, in the given equation b is:

$\begin{gathered} b=7 \\ b=-7 \end{gathered}$