Question

Question For the function f(x) = 8x^2 - 18x + 5, find x when f(x) = -4.

Answer 1

`x\text{ = 3/2 or x = 3/4}`Step-by-step explanation:

f(x) = 8x² - 18x + 5

f(x) = -4

replacing f(x) with -4 in the given function:

-4 = 8x² - 18x + 5

8x² - 18x + 5 + 4 = 0

8x² - 18x + 9 = 0

Using the almighty formula:

For ax² +bx + c = 0:

8x² - 18x + 9 = 0

a = 8, b= -18, c = 9

`x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`
`\begin{gathered} x\text{ = }\frac{-(-18)\pm\sqrt[]{(-18)^2-4(8)(9)}}{2(8)} \\ x\text{ = }\frac{18\pm\sqrt[]{324-288}}{16}=\frac{18\pm\sqrt[]{36}}{16} \end{gathered}`
`\begin{gathered} x=\frac{18\pm\sqrt[]{36}}{16}=(18\pm6)/(16) \\ x\text{ = }(18+6)/(16)or\text{ }(18-6)/(16) \\ x\text{ = 24/16 or 12/16} \\ x\text{ = 3/2 or x = 3/4} \end{gathered}`