Answer:
(x - [tex]\frac{5}{2} [/tex] )² + [tex]\frac{7}{4} [/tex]
Step-by-step explanation:
x² - 5x + 8
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 5x
x² + 2(- [tex]\frac{5}{2} [/tex] )x + [tex]\frac{25}{4} [/tex] - [tex]\frac{25}{4} [/tex] + 8
= (x - [tex]\frac{5}{2} [/tex] )² - [tex]\frac{25}{4} [/tex] + [tex]\frac{32}{4} [/tex]
= (x - [tex]\frac{5}{2} [/tex] )² + [tex]\frac{7}{4} [/tex]
