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

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

$4x^2 + 12x + 9 + 16x + 24 + 11 = 0$

$4x^2 + 28x + 44 = 0$

$x^2 + 7x + 11 = 0$

Use quadratic equation:

$a = 1 \ , \  b = 7 \  , \ c = 11$

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

$x = \dfrac{-6 \pm \sqrt{7^2 - 4(1)(11)}} {2}$

$x = \dfrac{-6 \pm \sqrt{5}} {2}$

$x = -3 + \dfrac{\sqrt{5} }{2} \ or \ x = -3 - \dfrac{\sqrt{5} }{2}$

$x = -1.88 \ or \ -4.12$