janikexo
30

# How do I solve the equation for "x" in this problem? (x-7)^2/3+1=10

$(x-7)^{\tfrac{2}{3}}+1=10\\ \sqrt[3]{(x-7)^2}=9\\ (x-7)^2=729\\ x-7=\sqrt{729} \vee x-7=-\sqrt{729}\\ x=7+27 \vee x=7-27\\ x=34 \vee x=-20$
${ \left( x-7 \right) }^{ \frac { 2 }{ 3 } }+1=10\\ \\ { \left( x-7 \right) }^{ \frac { 2 }{ 3 } }=9$ $\\ \\ { \left\{ { \left( x-7 \right) }^{ 2 } \right\} }^{ \frac { 1 }{ 3 } }=9\\ \\ { \left( x-7 \right) }^{ 2 }={ 9 }^{ 3 }$ $\\ \\ { \left( x-7 \right) }^{ 2 }=729\\ \\ x-7=\pm \sqrt { 729 } \\ \\ x-7=\pm 27\\ \\ x=7\pm 27$