Answer:
x=1 or x=-5
Step-by-step explanation:
The given function is
[tex]f(x) = {(x - 2)}^{2} - 9[/tex]
The solutions are the roots of the function.
This is where the graph of the function touches the x-axis.
We set the equation to zero to get:
[tex] {(x - 2)}^{2} - 9 = 0[/tex]
[tex] {(x - 2)}^{2} = 9[/tex]
We take square root to get:
[tex]{(x - 2)} = \pm \sqrt{9} [/tex]
[tex]x - 2= \pm 3[/tex]
[tex]x= 2 \pm 3[/tex]
[tex]x= 2 - 3 \: or \: x = 2 + 3[/tex]
[tex]x = - 1 \: or \: x = 5[/tex]
