Respuesta :
Answer:
x ≈ 18.7
Step-by-step explanation:
This is a big equation, so let's break it down a bit.
[tex]\frac{3}{2} \sqrt[4]{(2(x-6) ^3 )} +4=16[/tex]
Let's start by isolating the radical which is x.
So subtract 4 from both sides :
[tex]\frac{3}{2} \sqrt[4]{(2(x-6) ^3)}[/tex][tex]=12[/tex]
Now multiply both sides by 2 to get rid of the fraction :
[tex]3\sqrt[4]{(2(x-6)^3)} = 24[/tex]
Now divide both sides by 3 to get rid of the number out of the poly root :
[tex]\sqrt[4]{2(x-6) ^3}[/tex][tex]=8[/tex]
Now take both sides of the equation to the power of 4 :
[tex]2x^3 - 36x^2+216x-432=4096[/tex]
And lastly, solve :
[tex]x = 18.69920[/tex] which is rounded up to [tex]x[/tex] ≈ [tex]18.7[/tex]
