Question
Solve for all values of xx by factoring.
x, squared, minus, x, minus, 35, equals, minus, x, plus, 1
x
2
−x−35=
−x+1
x, squared, minus, x, minus, 35, equals, minus, x, plus, 1
x
2
−x−35=
−x+1
Answers
GPT-4o mini
To solve the equation \( x^2 - x - 35 = -x + 1 \), we first rearrange it by adding \( x \) and subtracting \( 1 \) from both sides:
\[
x^2 - x - 35 + x - 1 = 0
\]
This simplifies to:
\[
x^2 - 36 = 0
\]
Next, we can factor the left side of the equation:
\[
(x - 6)(x + 6) = 0
\]
Now, we set each factor to zero:
1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)
Thus, the solutions for the equation are:
\[
\boxed{6 \text{ and } -6}
\]
\[
x^2 - x - 35 + x - 1 = 0
\]
This simplifies to:
\[
x^2 - 36 = 0
\]
Next, we can factor the left side of the equation:
\[
(x - 6)(x + 6) = 0
\]
Now, we set each factor to zero:
1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)
Thus, the solutions for the equation are:
\[
\boxed{6 \text{ and } -6}
\]