Solve the equation by factoring.

xsquared2plus 3+3xnegative 10−10equals=0

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Part 1

A.

​{55​,negative 2−2​}

B.

​{negative 5−5​,1}

C.

​{55​,22​}

D.

​{negative 5−5​,22​}

To solve the quadratic equation by factoring, let's first clarify and rewrite it properly.

It seems you meant:

\[
x^2 + 3x - 10 = 0
\]

### Step 1: Factor the quadratic expression.

We need to factor the expression \(x^2 + 3x - 10\). To do this, we find two numbers that multiply to give \(-10\) (the constant term) and add up to \(3\) (the coefficient of \(x\)).

The two numbers that work are \(5\) and \(-2\), because:
- \(5 \times (-2) = -10\)
- \(5 + (-2) = 3\)

### Step 2: Write the factored form.

Now, we can factor the quadratic as:

\[
(x + 5)(x - 2) = 0
\]

### Step 3: Solve for \(x\).

To solve for \(x\), set each factor equal to zero:

1. \(x + 5 = 0 \quad \Rightarrow \quad x = -5\)
2. \(x - 2 = 0 \quad \Rightarrow \quad x = 2\)

### Final Answer:

The solutions are \(x = -5\) and \(x = 2\).

Thus, the correct answer is:

**D.** \(\{-5, 2\}\)

Would you like more details on any of these steps, or do you have further questions? 

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Here are 5 related questions for further practice:

1. How do you factor a quadratic equation in general form?
2. What methods can be used to solve a quadratic equation besides factoring?
3. What is the relationship between the roots and the coefficients of a quadratic equation?
4. How would you solve the equation \(x^2 + 5x + 6 = 0\)?
5. What is the significance of the discriminant in a quadratic equation?

**Tip:** Always check your factorization by expanding the factors to make sure you get the original quadratic expression!

Solve the equation by factoring: xsquared2plus 3+3xnegative 10−10equals=0

Solve the quadratic equation x^2 + 3x - 10 by factoring. This problem involves key algebraic concepts such as factoring quadratic equations and the zero-product property. Suitable for students in Grades 8-10, the solution provides a clear step-by-step breakdown.

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