Solve for all values of xx by factoring.    x^2-8x=-x

Let's solve the quadratic equation \( x^2 - 8x = -x \) by factoring.

### Step 1: Move all terms to one side
We begin by moving the \(-x\) from the right-hand side to the left-hand side:
\[
x^2 - 8x + x = 0
\]
Simplify the equation:
\[
x^2 - 7x = 0
\]

### Step 2: Factor the equation
Now, factor the left-hand side:
\[
x(x - 7) = 0
\]

### Step 3: Solve for \( x \)
For the product to be zero, either \( x = 0 \) or \( x - 7 = 0 \).

Thus, the solutions are:
\[
x = 0 \quad \text{or} \quad x = 7
\]

### Final Answer:
The solutions are \( x = 0 \) and \( x = 7 \).

Would you like any further details or have any questions?

Here are 5 related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. Can all quadratic equations be factored?
3. How would the solution change if the equation had a different constant term?
4. What are the key differences between factoring and completing the square?
5. How does factoring relate to the zero product property?

**Tip:** Always check your solutions by plugging them back into the original equation to verify correctness.

Solve for all values of x by factoring. x^2 - 8x = -x

Learn how to solve the quadratic equation x^2 - 7x = 0 by factoring. This detailed solution covers algebraic concepts like factoring and the zero product property. Perfect for students in Grades 8-10.

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