Solve for t.

Question

t^2 − 81 = –45

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

t =
or t =

Answer 1

To solve the equation

\[ t^2 - 81 = -45, \]

first, we add 81 to both sides:

\[ t^2 = -45 + 81. \]

Calculating the right side gives:

\[ t^2 = 36. \]

Next, we take the square root of both sides. Remember that taking the square root of a number can result in both a positive and a negative solution:

\[ t = \sqrt{36} \quad \text{or} \quad t = -\sqrt{36}. \]

Calculating the square root, we get:

\[ t = 6 \quad \text{or} \quad t = -6. \]

Thus, the final solutions are:

\[ t = 6 \quad \text{or} \quad t = -6. \]