Answer:
x = [tex]\frac{7}{2}[/tex] ± [tex]\frac{\sqrt{13} }{2}[/tex]
Step-by-step explanation:
Given
x² - 7x + 9 = 0 ( subtract 9 from both sides )
x² - 7x = - 9
Solve using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2( - [tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] = - 9 +
(x - [tex]\frac{7}{2}[/tex] )² = [tex]\frac{13}{4}[/tex] ( take the square root of both sides )
x - [tex]\frac{7}{2}[/tex] = ± [tex]\sqrt{\frac{13}{4} }[/tex] = ± [tex]\frac{\sqrt{13} }{2}[/tex] ( add
x = [tex]\frac{7}{2}[/tex] ± [tex]\frac{\sqrt{13} }{2}[/tex] = [tex]\frac{7+/-\sqrt{13} }{2}[/tex]
