Consider the given equation,
[tex]4x^2-100=0[/tex]Add 100 both sides,
[tex]\begin{gathered} 4x^2-100+100=0+100 \\ 4x^2=100 \end{gathered}[/tex]Divide by 4 both sides,
[tex]\begin{gathered} 4x^2\cdot\frac{1}{4}=100\cdot\frac{1}{4} \\ x^2=25 \end{gathered}[/tex]Take square roots both sides,
[tex]\begin{gathered} x=\pm\sqrt[]{25} \\ x=-5,5 \end{gathered}[/tex]Thus, the roots of the given equation are -5 and 5.
Therefore, option C is the correct choice.
