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
