Question

-81x^2 = -11
What are the solutions to the given equation?

Answer 1

To solve the equation \(-81x^2 = -11\), we first divide both sides by -1 to simplify it:

\[
81x^2 = 11
\]

Next, we divide both sides by 81:

\[
x^2 = \frac{11}{81}
\]

Now, we take the square root of both sides. Remember to consider both the positive and negative roots:

\[
x = \pm \sqrt{\frac{11}{81}}
\]

We can simplify the square root:

\[
x = \pm \frac{\sqrt{11}}{\sqrt{81}} = \pm \frac{\sqrt{11}}{9}
\]

Therefore, the solutions to the equation \(-81x^2 = -11\) are:

\[
x = \frac{\sqrt{11}}{9} \quad \text{and} \quad x = -\frac{\sqrt{11}}{9}
\]