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The equation provided is:

\[
2x^2 + 9x - 56 = 0
\]

To factor this quadratic equation, we need to find two numbers that multiply to the product of the coefficient of \(x^2\) (which is 2) and the constant term (-56), and add to the coefficient of \(x\) (which is 9).

The product is:
\[
2 \times (-56) = -112
\]

We need two numbers that multiply to \(-112\) and add to \(9\). These numbers are \(16\) and \(-7\).

Now, we can rewrite the middle term (9x) using these two numbers:

\[
2x^2 + 16x - 7x - 56 = 0
\]

Next, we group the terms:

\[
(2x^2 + 16x) + (-7x - 56) = 0
\]

Factor out the common terms from each group:

\[
2x(x + 8) - 7(x + 8) = 0
\]

Now, factor out the common binomial \((x + 8)\):

\[
(x + 8)(2x - 7) = 0
\]

So, the factored form of the quadratic equation is:

\[
(x + 8)(2x - 7) = 0
\]

### Solutions:

To find the values of \(x\), set each factor equal to zero:

1. \(x + 8 = 0 \implies x = -8\)
2. \(2x - 7 = 0 \implies x = \frac{7}{2}\)

Thus, the solutions are:

\[
x = -8 \quad \text{and} \quad x = \frac{7}{2}
\]

Would you like more details or have any questions?

### Related Questions:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the difference between factoring and using the quadratic formula?
3. How can you use factoring to solve quadratic equations in word problems?
4. What are the conditions under which a quadratic equation can be factored easily?
5. How do you recognize a perfect square trinomial?

### Tip:

When factoring quadratic equations, always check if you can factor out a greatest common factor (GCF) first to simplify your work.

Factor the quadratic equation: 2x^2 + 9x - 56 = 0

This step-by-step guide explains how to factor the quadratic equation 2x^2 + 9x - 56 = 0. Learn to solve by identifying factors and applying algebraic techniques, ideal for students in Grades 9-11.

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