Question

solve by factoring. (x - 2)(x + 7)= - 20 the solution set is { }. (type an integer or a simplified fraction. use a comma to separate answers as needed. type each

Explanation:

Step1: Expand the left - hand side

$(x - 2)(x + 7)=x^{2}+7x-2x - 14=x^{2}+5x - 14$
So the equation becomes $x^{2}+5x - 14=-20$.

Step2: Rearrange to standard quadratic form

Add 20 to both sides: $x^{2}+5x - 14 + 20=0$, which simplifies to $x^{2}+5x + 6=0$.

Step3: Factor the quadratic equation

We need to find two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3. So $x^{2}+5x + 6=(x + 2)(x+3)=0$.

Step4: Solve for x

Set each factor equal to zero:
If $x + 2=0$, then $x=-2$.
If $x + 3=0$, then $x=-3$.

Answer:

$-2,-3$