Question

What is the solution of the equation? 2^5 sqrt (x+6)^3+3 =19

Answer 1

`\bf 2^5√((x+6)^3)+3=19\implies 2^5√((x+6)^3)=16\implies √((x+6)^3)=\cfrac{16}{2^5} \\\\\\ √((x+6)^3)=\cfrac{16}{32}\implies √((x+6)^3)=\cfrac{1}{2}\implies \stackrel{\textit{squaring both sides}}{(x+6)^3=\left( \cfrac{1}{2} \right)^2} \\\\\\ (x+6)^3=\cfrac{1^2}{2^2}\implies (x+6)^3=\cfrac{1}{4}\implies \stackrel{\textit{taking }\sqrt[3]{\qquad }\textit{ to both sides}}{x+6=\sqrt[3]{\cfrac{1}{4}}} \\\\\\ x=\sqrt[3]{\cfrac{1}{4}}-6`

and if you plug that in your calculator, it'd give you -5.37003947505256341762.