Answer:
D. -2 and 8.
Explanation:
The initial expression is:
[tex]x^2-6x=16[/tex]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:
[tex]\begin{gathered} x^2-6x-16=16-16 \\ x^2-6x-16=0 \end{gathered}[/tex]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:
[tex](x-8)(x+2)=0[/tex]So, the solutions of the equation are:
[tex]\begin{gathered} x-8=0 \\ x-8+_{}8=0+8 \\ x=8 \\ or \\ x+2=0 \\ x+2-2=-2 \\ x=-2 \end{gathered}[/tex]Then, the answer is D. -2 and 8.
