Respuesta :
Step-by-step explanation:
We can write the given expression as follows
x^2+5x+9 = x^2 +5x +25/4 - 25/4 +9 = (x + 5/2)^2 + (36-25)/4
= (x + 5/2)^2 + 11/4 ok
a hug.
Answer:
(x + [tex]\frac{5}{2}[/tex] )² + [tex]\frac{11}{4}[/tex]
Step-by-step explanation:
given the expression
x² + 5x + 9
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{5}{2}[/tex] )² - ( [tex]\frac{5}{2}[/tex] )² + 9
= x² + 2 ([tex]\frac{5}{2}[/tex] )x + [tex]\frac{25}{4}[/tex] - [tex]\frac{25}{4}[/tex] + 9
= (x + [tex]\frac{5}{2}[/tex] )² - [tex]\frac{25}{4}[/tex] + [tex]\frac{36}{4}[/tex]
= (x + [tex]\frac{5}{2}[/tex] )² + [tex]\frac{11}{4}[/tex] ← in the form (x + a)² + b
with a = [tex]\frac{5}{2}[/tex] and b = [tex]\frac{11}{4}[/tex]
