Answer:
[tex]2\sqrt7,-2\sqrt7[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=4x^2-6[/tex]
And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):
[tex]106=4x^2-6[/tex]
Add 6 to both sides:
[tex]112=4x^2[/tex]
Divide both sides by 4:
[tex]x^2=28[/tex]
Take the square root of both sides:
[tex]x=\pm\sqrt{28}[/tex]
Simplify the square root:
[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]
So, those are the two values that will satisfy our requirement.
And we're done!
