Respuesta :
Answer:
x = -7 ±√5  /2
That is;
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Step-by-step explanation:
To find the solutions to the equation, we will follow the steps below
(2x + 3)² + 8(2x + 3) + 11 = 0 --------------------------------------------------------------(1)
let u = 2x + 3
we will replace 2x+ 3 by  u  in equation (1)
u² + 8u + 11 = 0  -----------------------------------------------------------------------------(2)
we will solve equation (2) using  the formula method
a=1 Â b=8 Â Â and c=11
u = -b ± √b² - 4ac  /2a
u = -8 ±√(-8)² - 4(1)(11)   /2(1)
u = -8 ±√64 - 44   /2
u = -8 ±√20   /2
u = -8/2  ± √20/2
u= -4 ± √20/2
u= -4 ± √5×4  /2
u= -4 ± 2√5 /2
u= -4 ± √5  ---------------------------------------------------------------------------(30
but u = 2x + 3
Substitute u =2x+3 in equation (3)
2x + 3 = -4 ± √5
subtract 3 from both-side of the equation
2x + 3-3 = -4 -3 ± √5
2x = -7±√5
Divide both-side of the equation by 2
2x/2 = -7 ±√5  /2
x = -7 ±√5  /2
