Question

solve by factoring. (x - 1)(x + 5)= - 8 the solution set is {}. (type an integer or a simplified fraction. use a comma to separate answers as needed)

Explanation:

Step1: Expand the left - hand side

$(x - 1)(x + 5)=x^{2}+5x-x - 5=x^{2}+4x - 5$
So the equation becomes $x^{2}+4x - 5=-8$.

Step2: Rearrange to standard quadratic form

Add 8 to both sides: $x^{2}+4x - 5 + 8=0$, which simplifies to $x^{2}+4x+3 = 0$.

Step3: Factor the quadratic equation

We need to find two numbers that multiply to 3 and add up to 4. The numbers are 1 and 3. So $x^{2}+4x + 3=(x + 1)(x+3)=0$.

Step4: Solve for x

Set each factor equal to zero:
If $x + 1=0$, then $x=-1$; if $x + 3=0$, then $x=-3$.

Answer:

$-1,-3$