Question
Solve for all values of xx by factoring.
x, squared, plus, 5, x, plus, 1, equals, 5, x, plus, 2
x
2
+5x+1=
5x+2
Answer
Attempt 1 out of 2
x, squared, plus, 5, x, plus, 1, equals, 5, x, plus, 2
x
2
+5x+1=
5x+2
Answer
Attempt 1 out of 2
Answers
GPT-4o mini
To solve the equation \(x^2 + 5x + 1 = 5x + 2\) by factoring, we start by rearranging the equation to one side.
1. Subtract \(5x\) and \(2\) from both sides:
\[
x^2 + 5x + 1 - 5x - 2 = 0
\]
This simplifies to:
\[
x^2 - 1 = 0
\]
2. Now we can factor the left side:
\[
(x - 1)(x + 1) = 0
\]
3. Set each factor equal to zero:
For \(x - 1 = 0\):
\[
x = 1
\]
For \(x + 1 = 0\):
\[
x = -1
\]
4. Therefore, the solutions are:
\[
\boxed{1 \text{ and } -1}
\]
1. Subtract \(5x\) and \(2\) from both sides:
\[
x^2 + 5x + 1 - 5x - 2 = 0
\]
This simplifies to:
\[
x^2 - 1 = 0
\]
2. Now we can factor the left side:
\[
(x - 1)(x + 1) = 0
\]
3. Set each factor equal to zero:
For \(x - 1 = 0\):
\[
x = 1
\]
For \(x + 1 = 0\):
\[
x = -1
\]
4. Therefore, the solutions are:
\[
\boxed{1 \text{ and } -1}
\]