Question

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve

Answer 1

Amswer:x= -41/20
Solutions:
(2x + 3)2 + 8(2x + 3) + 11 = 0
4x+6+16x+24+11=0
20x+41=0
20x=-41
x= -41/20

Answer 2

Answer:

The given expression in single variable is:

 $(2 x +3)^2 +8 \times (2 x +3) +11=0\\\\ 4x^2 +9 +2 \times 2 x \times 3+8 \times 2 x+8 \times 3+11=0\\\\4 x^2+12 x+16 x+9+24+11=0\\\\4x^2+28 x+44=0\\\\4 \times (x^2+7 x+11)=0\\\\x^2+7 x+11=0\\\\ x=\frac{-7\pm \sqrt{7^2-4 \times 11 \times 1}}{2 \times 1}\\\\x=\frac{-7\pm \sqrt{49-44}}{2}\\\\x=\frac{-7\pm \sqrt{5}}{2}$

⇒Used Distributive property of Multiplication with respect to Addition:

a × (b+c)=a ×b+a × c

⇒For, a Quadratic expression of the form

Ax² +Bx +C=0

Discriminant=D=B²-4 AC

$x=\frac{-B\pm \sqrt{D}}{2 A}$

There are two zeroes which are

$x_{1}=\frac{-7+ \sqrt{5}}{2}\\\\x_{2}=\frac{-7- \sqrt{5}}{2}$