The problem asks to find the solution set of two quadratic equations by factoring. The quadratic equations are: a) $x^2 + 9x + 14 = 0$ b) $x^2 - 4x = 12$

1. Problem Description

The problem asks to find the solution set of two quadratic equations by factoring. The quadratic equations are:

a) $x^2 + 9x + 14 = 0$

b) $x^2 - 4x = 12$

2. Solution Steps

a) $x^2 + 9x + 14 = 0$

We need to find two numbers that multiply to 14 and add up to

9. These numbers are 2 and

7. Therefore, we can factor the quadratic as:

$(x + 2)(x + 7) = 0$

Setting each factor to zero, we get:

$x + 2 = 0 \Rightarrow x = -2$

$x + 7 = 0 \Rightarrow x = -7$

The solution set is $\{-2, -7\}$.

b) $x^2 - 4x = 12$

First, rewrite the equation in standard quadratic form by subtracting 12 from both sides:

$x^2 - 4x - 12 = 0$

Now we need to find two numbers that multiply to -12 and add up to -

4. These numbers are -6 and

2. Therefore, we can factor the quadratic as:

$(x - 6)(x + 2) = 0$

Setting each factor to zero, we get:

$x - 6 = 0 \Rightarrow x = 6$

$x + 2 = 0 \Rightarrow x = -2$

The solution set is $\{6, -2\}$.

3. Final Answer

The solution set for a) is $\{-7, -2\}$.

The solution set for b) is $\{-2, 6\}$.