Question

Solve for y.

100y2 − 27 = –11

Write your answers as integers or as proper or improper fractions in simplest form.

y =
or y =

Answer 1

To solve the equation \(100y^2 - 27 = -11\), we first rearrange the equation by adding 27 to both sides:

\[
100y^2 = -11 + 27
\]
\[
100y^2 = 16
\]

Next, we divide both sides by 100:

\[
y^2 = \frac{16}{100}
\]

We can simplify \(\frac{16}{100}\) to \(\frac{4}{25}\):

\[
y^2 = \frac{4}{25}
\]

Now, we take the square root of both sides:

\[
y = \pm \sqrt{\frac{4}{25}}
\]

Calculating the square root:

\[
y = \pm \frac{\sqrt{4}}{\sqrt{25}} = \pm \frac{2}{5}
\]

Thus, the solutions for \(y\) are:

\[
y = \frac{2}{5} \quad \text{or} \quad y = -\frac{2}{5}
\]

So the final answers are:

\[
y = \frac{2}{5} \quad \text{or} \quad y = -\frac{2}{5}
\]