Question

What are the solutions to x2 - 6x = 16? A.-2 B.2 and 8 C.-8 and 2 D. -2 and 8

Answer 1

D. -2 and 8.

Step-by-step explanation:

The initial expression is:

`x^2-6x=16`

To find the solutions we need to write the expression in the quadratic form:

ax² + bx + c = 0 , then factorize and finally solve for x.

So, subtract 16 from both sides of the equation:

`\begin{gathered} x^2-6x-16=16-16 \\ x^2-6x-16=0 \end{gathered}`

Now, we need to factorize, so we need to find two numbers such that the sum of these numbers is -6 and the multiplication is -16. These numbers are -8 and 2, therefore:

`(x-8)(x+2)=0`

So, the solutions of the equation are:

`\begin{gathered} x-8=0 \\ x-8+_{}8=0+8 \\ x=8 \\ or \\ x+2=0 \\ x+2-2=-2 \\ x=-2 \end{gathered}`

Then, the answer is D. -2 and 8.