Question

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Answer 1

Answer:
The second choice is the correct one

Explanation:
(2x+3)^2 + 8(2x+3) + 11 = 0
To use the u substitution, we will assume that:
2x + 3 = u

Substitute with this in the given expression, we will get:
u^2 + 8u + 11 = 0 

The general form of the second degree equation is:
ax^2 + bx + c = 0

Comparing the expression we reached with the general one, we will find that:
a = 1
b = 8
c = 11

The roots can be found using the rule found in the attached picture.
This means that, for the given expression:
u = -4 ± √5 

Now, we have:
u = 2x+3
This means that:
at u = -4 + √5 
2x + 3 = -4 + √5 
2x = -7 + √5
x = (-7 + √5) / 2

at u = -4 - √5 
2x + 3 = -4 - √5 
2x = -7 - √5
x = (-7 - √5) / 2

This means that, for the given expression:
x = (-7 ± √5 ) / 2

Hope this helps :)

Answer 2

(2x + 3) ^ 2 + 8 (2x + 3) + 11 = 0
 Using substitution we have:
 u = 2x + 3
 We rewrite:
 (u) ^ 2 + 8 (u) + 11 = 0
 We use resolvent:
 u = (- b +/- root (b ^ 2 - 4ac)) / (2a)
 We replace:
 u = (- (8) +/- root ((8) ^ 2 - 4 (1) (11))) / (2 (1))
 u = (- (8) +/- root (64 - 44)) / (2)
 u = (- (8) +/- root (20)) / (2)
 u = (- (4) +/- root (5))
 We return the change:
 u = (- (4) +/- root (5)) = 2x + 3
 We clear x:
 x = (- (7) +/- root (5)) / 2
 Answer:
 x = (- (7) +/- root (5)) / 2
 (option2)