which is a solution to (x - 2)(x + 10) = 13?\no x = 3\no x = 8\no x = 10\no x = 11

Explanation:

Step1: Expand the left - hand side

$(x - 2)(x + 10)=x^{2}+10x-2x - 20=x^{2}+8x - 20$. So the equation becomes $x^{2}+8x - 20 = 13$.

Step2: Rearrange to standard quadratic form

$x^{2}+8x-20 - 13=0$, which simplifies to $x^{2}+8x - 33 = 0$.

Step3: Factor the quadratic equation

We need to find two numbers that multiply to - 33 and add up to 8. The numbers are 11 and - 3. So $x^{2}+8x - 33=(x + 11)(x - 3)=0$.

Step4: Solve for x

Setting each factor equal to zero gives $x+11 = 0$ or $x - 3=0$. So $x=-11$ or $x = 3$.

Answer:

$x = 3$ (corresponding to the option in the multiple - choice list)