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 that multiply to 14 and add up to

9. These numbers are 2 and

7. So, we can factor the quadratic equation as:

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

Now, we set each factor equal to zero:

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

Solving for $x$:

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

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

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

First, we rewrite the equation in standard 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. So, we can factor the quadratic equation as:

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

Now, we set each factor equal to zero:

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

Solving for $x$:

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

The solution set is {6, -2}.

3. Final Answer

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

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