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

(2x+3)2+8(2x+3)+11=0

(4x+6)+(16x+24)+11=0

20x+30+11=0

20x+41=0

20x=-41

x=-41/20

Answer 2

(2x + 3)² + 8(2x + 3) + 11 = 0

4x² + 12x + 9 + 16x + 24 + 11 = 0

4x² + 28x + 44 = 0

x² + 7x + 11  = 0

Using quadratic formula:

$x = \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Sub a = 1, b = 7 and c = 11:

$x = \dfrac{-7\pm \sqrt{7^2-4(1)(11)} }{2(1)}$

$x = \dfrac{-14\pm \sqrt{49-44} }{2}$

$x = \dfrac{-14\pm \sqrt{5} }{2}$

$x = -7 + \sqrt{5} \ \ or \ \ x = -7 - \sqrt{5}$

$x = -4.76 \ \ or \ \ x = -9.23$