Question
Solve for all values of xx by factoring.
x, squared, minus, 81, equals, 0
x
2
−81=
0
x, squared, minus, 81, equals, 0
x
2
−81=
0
Answers
GPT-4o mini
To solve the equation \( x^2 - 81 = 0 \) by factoring, we can recognize that \( 81 \) is a perfect square, specifically \( 9^2 \). This allows us to rewrite the equation as a difference of squares:
\[
x^2 - 9^2 = 0
\]
We can factor this using the difference of squares formula, \( a^2 - b^2 = (a - b)(a + b) \):
\[
(x - 9)(x + 9) = 0
\]
Now we set each factor equal to zero:
1. \( x - 9 = 0 \)
2. \( x + 9 = 0 \)
Solving these equations gives:
1. \( x = 9 \)
2. \( x = -9 \)
Thus, the solutions to the equation \( x^2 - 81 = 0 \) are:
\[
\boxed{9} \quad \text{and} \quad \boxed{-9}
\]
\[
x^2 - 9^2 = 0
\]
We can factor this using the difference of squares formula, \( a^2 - b^2 = (a - b)(a + b) \):
\[
(x - 9)(x + 9) = 0
\]
Now we set each factor equal to zero:
1. \( x - 9 = 0 \)
2. \( x + 9 = 0 \)
Solving these equations gives:
1. \( x = 9 \)
2. \( x = -9 \)
Thus, the solutions to the equation \( x^2 - 81 = 0 \) are:
\[
\boxed{9} \quad \text{and} \quad \boxed{-9}
\]