Question

If (3x^2)+7=0 then (x-1/3)^2

Answer 1

$3x^2+7=0 \\x^2=- \frac{7}{3} \\x=\pm \sqrt{-\frac{7}{3} } \\x=\pm i \sqrt{\frac{7}{3} } \\ \\(x- \frac{1}{3} )^2=x^2- \frac{2}{3}x+ \frac{1}{9} =- \frac{7}{3} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9} = \\=- \frac{21}{9} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9} \\=- \frac{20}{9} \mp i\frac{2}{3} \sqrt{\frac{7}{3} }$