Question

Solve for all values of xx by factoring.
x, squared, plus, 4, equals, 5
x
2
+4=
5

Answer 1

To solve the equation \( x^2 + 4 = 5 \) by factoring, we first need to rearrange the equation to set it to zero:

1. Subtract 5 from both sides:

\[
x^2 + 4 - 5 = 0
\]

This simplifies to:

\[
x^2 - 1 = 0
\]

2. Now, we can factor the equation. The expression \( x^2 - 1 \) is a difference of squares, which can be factored as follows:

\[
(x - 1)(x + 1) = 0
\]

3. Now, we can set each factor equal to zero:

\[
x - 1 = 0 \quad \text{or} \quad x + 1 = 0
\]

4. Solving these equations gives us:

\[
x = 1 \quad \text{or} \quad x = -1
\]

Thus, the solutions are:

\[
\boxed{1} \quad \text{and} \quad \boxed{-1}
\]