Question

x2+3x+9=0 solve by completing square ​

Answer 1

${x}^{2} + 3x + 9 = 0 \\ \\ {x}^{2} + 2 \times \frac{3}{2} x + 9 = 0 \\ \\ {x}^{2} + 2 \times \frac{3}{2} x + \frac{9}{4} + 9 - \frac{9}{4} = 0 \\ \\ {(x + \frac{3}{2}) }^{2} = - \frac{27}{4} \\ \\ {(x + \frac{3}{2} )}^{2} = {( \sqrt{3} )}^{2} \times {( \frac{3}{2} )}^{2} {i}^{2} \\ \\ x + \frac{3}{2} = | \frac{3 \sqrt{3} }{2}i | \\ \\ x = \frac{3}{2} (1 - \sqrt{3} i) \\ \\ x = \frac{3}{2} (1 + \sqrt{3} i) \\ \\ {i}^{2} = - 1$

hope it helps.