Answer:
see explanation
Step-by-step explanation:
Given
x² - 9x + 4 = 0 ( subtract 4 from both sides )
x² - 9x = - 4
Using the method of completing the square
Add ( half the coefficient of the x- term )² to both sides
x² +2 (- [tex]\frac{9}{2}[/tex])x + [tex]\frac{81}{4}[/tex] = - 4 + [tex]\frac{81}{4}[/tex]
(x - [tex]\frac{9}{2}[/tex])² = [tex]\frac{65}{4}[/tex]
Take the square root of both sides
x - [tex]\frac{9}{2}[/tex] = ± [tex]\sqrt{\frac{65}{4} }[/tex] = ± [tex]\frac{1}{2}[/tex][tex]\sqrt{65}[/tex]
Add [tex]\frac{9}{2}[/tex] to both sides
x = [tex]\frac{9}{2}[/tex] ± [tex]\frac{1}{2}[/tex][tex]\sqrt{65}[/tex] ← exact solutions
