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.`