Question

Does anyone know this answer??

Answer 1

For this case we have the following equation:

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

Let $u = 2x + 3$

We have:

$u ^ 2 + 8u + 11 = 0$

By definition, given an equation of the form $ax ^ 2 + bx + c = 0$

The quadratic formula, to find the solution can be written as:

$x = \frac{-b+/-\sqrt{b ^ 2-4 (a) (c)} }{2(a)}$

In this case we have:

$a = 1\\b = 8\\c = 11$

Substituting in the quadratic formula we have:

See attached image

Answer:

Option B

Answer 2

x = (- 7 ± √5) / 2

use the substitution u = 2x + 3

equation can now be written as

u² + 8u + 11 = 0

solve for u using the quadratic formula with a = 1, b = 8 and c = 11

u = ( - 8 ± √( 64 - 44 ) )/2

  = ( - 8 ± √20 )/2 = ( - 8 ± 2√5 ) / 2 = - 4 ± √5

change the variable back into terms of  x

2x + 3 = - 4 ± √5 ( subtract 3 from both sides )

2x = - 7 ± √5 ( divide both sides by 2 )

x = ( - 7 ± √5 ) / 2