Answer: [tex]\bold{c)\quad x=\pm \dfrac{\sqrt{26}}{2}\qquad \qquad d)\quad x=\pm 2\sqrt3}[/tex]
Step-by-step 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
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(0)\pm \sqrt{(0)^2-4(2)(-13)}}{2(2)}\\\\\\.\quad =\pm\dfrac{\sqrt{104}}{4}\\\\\\.\quad =\pm \dfrac{2\sqrt{26}}{4}\\\\\\.\quad =\large\boxed{\pm \dfrac{\sqrt{26}}{2}}[/tex]
d) 11 + 5 = 2x² - 8
0 = 2x² - 24 (subtracted 16 from both sides)
--> 0 = 2x² + 0x - 24 --> a = 2, b = 0, c = -24
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(0)\pm \sqrt{(0)^2-4(2)(-24)}}{2(2)}\\\\\\.\quad =\pm\dfrac{\sqrt{192}}{4}\\\\\\.\quad =\pm \dfrac{8\sqrt{3}}{4}\\\\\\.\quad =\large\boxed{\pm 2\sqrt3}[/tex]
