Question

I don’t know how to solve c and d.
I’m supposed to use the quadratic formula.

Answer 1

Answer:
`\bold{c)\quad x=\pm (√(26))/(2)\qquad \qquad d)\quad x=\pm 2\sqrt3}`

Explanation:

It is much easier to use the square root method but since you requested the quadratic formula, I will solve it using that method.

First, replace g(x) with 0 for letter c and 11 for letter d. Then simplify and move everything to one side so the equation is equal to zero. Then plug in the a, b, and c values into the quadratic formula to solve for x.

g(x) + 5 = 2x² - 8

c) 0 + 5 = 2x² - 8

0 = 2x² - 13 (subtracted 5 from both sides)

--> 0 = 2x² + 0x - 13 --> a = 2, b = 0, c = -13

`x=(-b\pm √(b^2-4ac))/(2a)\\\\\\x=(-(0)\pm √((0)^2-4(2)(-13)))/(2(2))\\\\\\.\quad =\pm(√(104))/(4)\\\\\\.\quad =\pm (2√(26))/(4)\\\\\\.\quad =\large\boxed{\pm (√(26))/(2)}`

d) 11 + 5 = 2x² - 8

0 = 2x² - 24 (subtracted 16 from both sides)

--> 0 = 2x² + 0x - 24 --> a = 2, b = 0, c = -24

`x=(-b\pm √(b^2-4ac))/(2a)\\\\\\x=(-(0)\pm √((0)^2-4(2)(-24)))/(2(2))\\\\\\.\quad =\pm(√(192))/(4)\\\\\\.\quad =\pm (8√(3))/(4)\\\\\\.\quad =\large\boxed{\pm 2\sqrt3}`