The problem asks to find the solution set for the given quadratic equations by factorization. a) $x^2 + 9x + 14 = 0$ b) $x^2 - 4x = 12$

1. Problem Description

The problem asks to find the solution set for the given quadratic equations by factorization.

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 whose product is 14 and whose sum is

9. These numbers are 2 and

7. So, we can factor the equation as:

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

Then, we solve for $x$ by setting each factor to zero:

$x + 2 = 0$ or $x + 7 = 0$

$x = -2$ or $x = -7$

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

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

First, rewrite the equation as:

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

We need to find two numbers whose product is -12 and whose sum is -

4. These numbers are -6 and

2. So, we can factor the equation as:

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

Then, we solve for $x$ by setting each factor to zero:

$x - 6 = 0$ or $x + 2 = 0$

$x = 6$ or $x = -2$

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

3. Final Answer

a) $\{-2, -7\}$

b) $\{6, -2\}$