Answer:
x = 2 or x = -8 (d)
Step-by-step explanation:
Find two factors of 16 which differ by 6. The pair 8,2 works in that 8 × 2 = 16 and 8 - 2 = 6.
Hence we find:
[tex]0 = x^2+6x-16 = (x+8)(x-2)[/tex]
So x = 2 or x = -8
Alternatively, complete the square then use the difference of squares identity:
[tex]a^2-b^2 = (a-b)(a+b)[/tex]
with [tex]a = (x+3)[/tex] and [tex]b=5[/tex] as follows:
[tex]0 = x^2+6x-16[/tex]
[tex]=(x+3)^2-9-16[/tex]
[tex]=(x+3)^2-25[/tex]
[tex]=(x+3)^2-5^2[/tex][tex]=((x+3)-5)((x+3)+5)[/tex]
[tex]=(x-2)(x+8)[/tex]
Hence zeros [tex]x=2[/tex] and [tex]x=-8[/tex]
Subjects:
Algebra Quadratic Equations and Functions Comparing Methods for Solving Quadratics
