Now, we group the terms and factor out the common factors from each pair. From the first two terms, x² + 2x, we factor out x. From the last two terms, -x - 2, we factor out -1. This gives us x(x+2) - 1(x+2) = 0.

Now, we group the terms and factor out the common factors from each pair. From the first two terms, x² + 2x, we factor out x. From the last two terms, -x - 2, we factor out -1. This gives us x(x+2) - 1(x+2) = 0.

Write the solution set of the equation $x^2 + x - 2 = 0$ in roster form.

Answer: $\{1, -2\}$

Step-by-step solution

Step 1: Factor the quadratic equation

To find the solutions of the quadratic equation $x^2 + x - 2 = 0$ , we can factor the quadratic expression. We look for two numbers that multiply to $-2$ and add up to $1$ . These numbers are $2$ and $-1$ . So, we can rewrite the middle term $x$ as $2x - x$ .

Step 2: Group terms and factor out common factors

Now, we group the terms and factor out the common factors from each pair. From the first two terms, $x^2 + 2x$ , we factor out $x$ . From the last two terms, $-x - 2$ , we factor out $-1$ . This gives us $x(x+2) - 1(x+2) = 0$ .

Step 3: Factor out the common binomial

We can see that $(x+2)$ is a common binomial factor in both terms. Factoring out $(x+2)$ leaves us with $(x-1)(x+2) = 0$ .

Step 4: Solve for x

For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$ . This gives us $x-1=0$ , which means $x=1$ , and $x+2=0$ , which means $x=-2$ .

Step 5: Write the solution set in roster form

The solution set consists of all values of $x$ that satisfy the equation. In roster form, we list these values within curly braces. So, the solution set is $\{1, -2\}$ .

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Write the solution set of the equation x2+x−2=0x^2 + x - 2 = 0x2+x−2=0 in roster form.