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The given equation is:

\[
x^2 - x - 35 = -x + 1
\]

### Step 1: Simplify the equation
We want to bring all terms to one side of the equation, so let's move everything to the left side by adding \(x\) and subtracting 1 from both sides:

\[
x^2 - x - 35 + x - 1 = 0
\]

Simplify the terms:

\[
x^2 - 36 = 0
\]

### Step 2: Solve by factoring
Now, we have a difference of squares:

\[
x^2 - 36 = (x - 6)(x + 6)
\]

### Step 3: Set each factor equal to zero

\[
x - 6 = 0 \quad \text{or} \quad x + 6 = 0
\]

Solving these equations:

\[
x = 6 \quad \text{or} \quad x = -6
\]

### Final Answer:
The solutions are \(x = 6\) and \(x = -6\).

Would you like more details or have any questions?

### Related Questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What is the difference of squares and how is it used in factoring?
3. How do you solve quadratic equations by completing the square?
4. Can all quadratic equations be solved by factoring?
5. How can we check the solutions of a quadratic equation?

### Tip:
When solving quadratic equations, always first check if it can be factored easily. This saves time compared to other methods like completing the square or using the quadratic formula.

Solve for all values of x by factoring: x^2 - x - 35 = -x + 1

This page explains how to solve the quadratic equation x^2 - x - 35 = -x + 1 by factoring. It covers key algebraic concepts such as the difference of squares and factoring techniques. Suitable for Grades 8-10.

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