Simplify the following. $$ x=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(1)(3)}}{2(1)} $$ $$ x=\square \pm \sqrt{\square} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression

$$
x = \frac{-(-8) \pm \sqrt{(-8)^{2}-4(1)(3)}}{2(1)},
$$

we start by simplifying each part step by step.

1. **Simplify $$-(-8)$$**:
   $$
   -(-8) = 8.
   $$

2. **Calculate $$(-8)^{2}$$**:
   $$
   (-8)^{2} = 64.
   $$

3. **Calculate $$4(1)(3)$$**:
   $$
   4(1)(3) = 12.
   $$

4. **Combine the results in the square root**:
   $$
   (-8)^{2} - 4(1)(3) = 64 - 12 = 52.
   $$

5. **Now substitute back into the expression for $$x$$**:
   $$
   x = \frac{8 \pm \sqrt{52}}{2}.
   $$

6. **Simplify $$\sqrt{52}$$**:
   $$
   \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}.
   $$

7. **Substitute $$\sqrt{52}$$ back into the expression**:
   $$
   x = \frac{8 \pm 2\sqrt{13}}{2}.
   $$

8. **Now simplify the fraction**:
   $$
   x = \frac{8}{2} \pm \frac{2\sqrt{13}}{2} = 4 \pm \sqrt{13}.
   $$

Thus, we can express $$x$$ in the required form:

$$
x = 4 \pm \sqrt{13}.
$$

So, the final answer is:

$$
x = 4 \pm \sqrt{13}.
$$
$$ x = 4 \pm \sqrt{13} $$.

Simplify the following. \( x=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(1)(3)}}{2(1)} \) \( x=\square \pm \sqrt{\square} \)