Given the functions:
[tex]\begin{gathered} f(x)=\sqrt[]{5x+25}-1 \\ g(x)=x^2-2x-3 \end{gathered}[/tex]
Solve the equations means finding the values of x provided that f(x) = g(x)
so,
[tex]x^2-2x-3=\sqrt[]{5x+25}-1[/tex]
Make the square root alone on the right-side
[tex]\begin{gathered} x^2-2x-3+1=\sqrt[]{5x+25} \\ x^2-2x-2=\sqrt[]{5x+25} \end{gathered}[/tex]
Square both sides to eliminate the square root:
[tex](x^2-2x-2)^2=5x+25[/tex]
Simplifying the equation:
[tex]\begin{gathered} x^2(x^2-2x-2)-2x(x^2-2x-2)-2(x^2-2x-2)=5x+25 \\ x^4-2x^3-2x^2-2x^3+4x^2+4x-2x^2+4x+4=5x+25 \\ x^4-4x^3+3x-21=0 \end{gathered}[/tex]
Solve the last equation to find the values of x
We can use the calculator to find the values of x
So,
[tex]x=-1.66,or,x=4.12[/tex]
Rounding to the nearest tenth
So, the answer will be x = {-1.7, 4.1 }
