Question

Solve −2x2 − 16x − 44 = 0. (2 points) Solving Quadratic Equations with Complex Solutions

Answer 1

Answer:

x = -4 + i√6 and x = -4-i√6

Step-by-step explanation:

Solution for quadratic equation

x = [-b ± √(b² - 4ac)]/2a

Here the quadratic equation is

-2x² - 16x -44 = 0

To find the solution of equation

Here a = -2, b = -16 and c = -44

x = [-b ± √(b² - 4ac)]/2a

x =  [--16 ± √((-16)² - 4*-2*-44)]/2*-2

x = [16 ± √(256 - 352)]/-4

x =  [16 ± 4i√6]/-4

x = -(4 ± i√6)

x = -4 + i√6 and x = -4-i√6

Answer 2

Answer:

$\large\boxed{x=-4-i\sqrt6\ \vee\ x=-4+i\sqrt6}$

Step-by-step explanation:

$-2x^2-16x-44=0\qquad\text{divide both sides by (-2)}\\\\x^2+8x+22=0\\\\\text{Use the quadratic formula of}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=8,\ c=22\\\\b^2-4ac=8^2-4(1)(22)=64-88=-24\\\\\sqrt{-24}=\sqrt{(4)(6)(-1)}=\sqrt4\cdot\sqrt6\cdot\sqrt{-1}=2\cdot\sqrt6\cdot i=2i\sqrt6\\\\x_1=\dfrac{-8-2i\sqrt6}{2(1)}=\dfrac{-8}{2}-\dfrac{2i\sqrt6}{2}=-4-i\sqrt6\\\\x_2=\dfrac{-8+2i\sqrt6}{2(1)}=\dfrac{-8}{2}+\dfrac{2i\sqrt6}{2}=-4+i\sqrt6$