Let $$ f(x)=x^{2}+2 x $$ Solve $$ f(x)=8 $$ a) 80 b) 1,8 c) 8 d) $$ -4,2 $$ e) $$ -2,4 $$

Question

UpStudy AI · Accepted Answer

1. Write the equation $$ f(x)=8 $$ in terms of $$ x $$:

$$
   x^2 + 2x = 8
   $$

2. Rearrange the equation to standard quadratic form:

$$
   x^2 + 2x - 8 = 0
   $$

3. Solve the quadratic equation using the quadratic formula:

$$
   x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{2a}
   $$
   
   Here, $$ a = 1 $$, $$ b = 2 $$, and $$ c = -8 $$.

4. Calculate the discriminant:

$$
   \Delta = b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36
   $$

5. Find the solutions:

$$
   x = \frac{{-2 \pm \sqrt{36}}}{2} = \frac{{-2 \pm 6}}{2}
   $$
   
   - For $$ + $$:

$$
     x = \frac{-2 + 6}{2} = \frac{4}{2} = 2
     $$
     
   - For $$ - $$:

$$
     x = \frac{-2 - 6}{2} = \frac{-8}{2} = -4
     $$

6. The solutions are $$ x = -4 $$ and $$ x = 2 $$.

Thus, the correct answer is option d) $$ -4,2 $$.
The solutions are $$ x = -4 $$ and $$ x = 2 $$, so the answer is d) $$ -4,2 $$.

Let \( f(x)=x^{2}+2 x \) Solve \( f(x)=8 \) a) 80 b) 1,8 c) 8 d) \( -4,2 \) e) \( -2,4 \)