which is a solution to the equation? (x - 3)(x - 5) = 35\no x = -8\no x = -5\no x = 2\no x = 10

Answer:

D. $x = 10$

Explanation:

Step1: Expand the left - hand side

$(x - 3)(x - 5)=x^{2}-5x-3x + 15=x^{2}-8x + 15$ So the equation becomes $x^{2}-8x + 15=35$.

Step2: Rearrange to standard quadratic form

Subtract 35 from both sides: $x^{2}-8x+15 - 35=0$, which simplifies to $x^{2}-8x - 20=0$.

Step3: Factor the quadratic equation

We need two numbers that multiply to - 20 and add up to - 8. These numbers are - 10 and 2. So $x^{2}-8x - 20=(x - 10)(x+2)=0$.

Step4: Solve for x

Using the zero - product property, if $(x - 10)(x + 2)=0$, then $x-10 = 0$ or $x + 2=0$. Solving $x-10 = 0$ gives $x = 10$, and solving $x + 2=0$ gives $x=-2$. Among the given options, $x = 10$ is the solution.