Solve the quadratic by factoring.
x, squared, plus, 12, x, minus, 70, equals, 9, x
x 
2
 +12x−70=9x

We are given the quadratic equation:

\[
x^2 + 12x - 70 = 9x
\]

### Step 1: Rearrange the equation
First, move all terms to one side of the equation:

\[
x^2 + 12x - 70 - 9x = 0
\]

Simplify:

\[
x^2 + 3x - 70 = 0
\]

### Step 2: Factor the quadratic expression
We need to find two numbers that multiply to give -70 and add to give 3. The numbers are 10 and -7 because:

\[
10 \times (-7) = -70 \quad \text{and} \quad 10 + (-7) = 3
\]

So, we can factor the quadratic as:

\[
(x + 10)(x - 7) = 0
\]

### Step 3: Solve for \( x \)
Set each factor equal to zero:

\[
x + 10 = 0 \quad \text{or} \quad x - 7 = 0
\]

Solving these gives:

\[
x = -10 \quad \text{or} \quad x = 7
\]

### Final Answer:
The solutions to the equation are \( x = -10 \) and \( x = 7 \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you verify the solutions of a factored quadratic equation?
2. What is the importance of factoring in solving quadratic equations?
3. What are other methods to solve quadratic equations besides factoring?
4. Can all quadratic equations be solved by factoring?
5. How does the discriminant relate to the number of solutions in a quadratic equation?

**Tip:** Always check if a quadratic equation can be simplified before factoring to make the process easier.

Solve the quadratic by factoring. x^2 + 12x - 70 = 9x

Learn how to solve the quadratic equation x^2 + 12x - 70 = 9x by factoring. This problem explores algebraic concepts such as factoring, quadratic equations, and the Zero Product Property, providing a clear step-by-step solution. Ideal for students in Grades 8-10.

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