Please help serious answers only

Answer:

#4          x = 3 ± i√31

                       2

Step-by-step explanation:

Solve by completing the square

  x² - 3x + 10 = 0    

  x² - 3x       =  -10

 x² - 3x + 9/4  =  -10 + 9/4       half of 3 and square the answer (half of 3 = 3/2  

                                                 and square the number   (3/2)²  = 9/4    

x² - 3x + 9/4  =  -31/4

[tex](x - \frac{3}{2} )^2 = \frac{-31}{4}[/tex]

[tex]\sqrt{(x-\frac{3}{2})^2 } =\sqrt{\frac{-31}{4} }[/tex]

[tex]x - \frac{3}{2} = \frac{i\sqrt{31} }{2}[/tex]  

x = 3/2 ±  i[tex]\sqrt{31}[/tex] /2

x = 3 ± i√31

          2

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