Question

Completing the square x^{2}+3×=0

Answer 1

${ x }^{ 2 }+3x=0\\ \\ { \left( x+\frac { 3 }{ 2 } \right) }^{ 2 }-{ \left( \frac { 3 }{ 2 } \right) }^{ 2 }=0\\ \\ { \left( x+\frac { 3 }{ 2 } \right) }^{ 2 }-\frac { 9 }{ 4 } =0$

$\\ \\ { \left( x+\frac { 3 }{ 2 } \right) }^{ 2 }=\frac { 9 }{ 4 } \\ \\ x+\frac { 3 }{ 2 } =\pm \frac { \sqrt { 9 } }{ \sqrt { 4 } } \\ \\ x+\frac { 3 }{ 2 } =\pm \frac { 3 }{ 2 } \\ \\ x=-\frac { 3 }{ 2 } \pm \frac { 3 }{ 2 } \\ \\ \therefore \quad x=0,\quad and\quad x=-3.$