Question

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

Answer 1

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

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=(-b\pm√(b^2-4ac))/(2a)\\\\a=1,\ b=8,\ c=22\\\\b^2-4ac=8^2-4(1)(22)=64-88=-24\\\\√(-24)=√((4)(6)(-1))=\sqrt4\cdot\sqrt6\cdot√(-1)=2\cdot\sqrt6\cdot i=2i\sqrt6\\\\x_1=(-8-2i\sqrt6)/(2(1))=(-8)/(2)-(2i\sqrt6)/(2)=-4-i\sqrt6\\\\x_2=(-8+2i\sqrt6)/(2(1))=(-8)/(2)+(2i\sqrt6)/(2)=-4+i\sqrt6`

Answer 2

x = -4 + i√6 and x = -4-i√6

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