Question

Solve the following equations x²+x+1 =0​

Answer 1

Answer:

$by \: completing \: square \\ {x}^{2} + x + 1 = 0 \\ {x}^{2} + 2x \times \frac{1}{ 2 } + \frac{1}{ {2}^{2} } - \frac{1}{ {2}^{2} } + 1 = 0 \\ (x + \frac{1}{2} ) {}^{2} - \frac{1}{4} + 1 = 0 \\ (x + \frac{1}{2} ) {}^{2} + \frac{3}{4 } = 0 \\ (x + \frac{1}{2} + \frac{ \sqrt{3}i }{2} )(x + \frac{1}{2} - \frac{ \sqrt{3} i}{2} ) = 0 \\ so \: \\ x = - ( \frac{1 + \sqrt{3} i}{2} ) \\ or \: - ( \frac{1 - \sqrt{3}i }{2} ) \\ < < i = \sqrt{ - 1} > >$