Question

QuestionFor the function f(x) = 8x2+18x + 5, find x when f(x) = -4.

Answer 1

So,

Given:

`f(x)=8x^2+18x+5`

We want to find the value of x when f(x) = -4.

For this, we could replace:

`\begin{gathered} 8x^2+18x+5=-4 \\ 8x^2+18x+9=0 \end{gathered}`

Now, let's solve this quadratic equation:

We could apply the quadratic formula as follows;

Given a quadratic equation of the form:

`ax^2+bx+c=0`

The solutions of this equation can be found using the following formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

If we replace the values of our equation, these are:

a=8

b=18

c=9

Thus,

`\begin{gathered} x=\frac{-18\pm\sqrt[]{18^2-4(8)(9)}}{2(8)} \\ \\ x=\frac{-18\pm\sqrt[]{36}}{16}\to\begin{cases}x_1=(-18+6)/(16)=(-12)/(16)=-(3)/(4) \\ x_2=(-18-6)/(16)=(-24)/(16)=-(3)/(2)\end{cases} \end{gathered}`

Therefore, the values of x are -3/2 and -3/4