$$ \Rightarrow \quad \partial x ^ { 2 } - 5 x + 4 = 0 $$

Question

UpStudy AI · Accepted Answer

It looks like you have the quadratic equation:

$$
x^{2} - 5x + 4 = 0
$$

Let's solve for $$ x $$.

### Method 1: Factoring

We can try to factor the quadratic equation:

$$
x^{2} - 5x + 4 = 0
$$

Find two numbers that multiply to $$ +4 $$ and add up to $$ -5 $$. These numbers are $$ -1 $$ and $$ -4 $$.

$$
(x - 1)(x - 4) = 0
$$

Set each factor equal to zero:

$$
x - 1 = 0 \quad \Rightarrow \quad x = 1
$$
$$
x - 4 = 0 \quad \Rightarrow \quad x = 4
$$

### Method 2: Quadratic Formula

Alternatively, you can use the quadratic formula:

$$
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
$$

For the equation $$ x^{2} - 5x + 4 = 0 $$, the coefficients are:
- $$ a = 1 $$
- $$ b = -5 $$
- $$ c = 4 $$

Plugging these into the formula:

$$
x = \frac{-(-5) \pm \sqrt{(-5)^{2} - 4 \cdot 1 \cdot 4}}{2 \cdot 1} = \frac{5 \pm \sqrt{25 - 16}}{2} = \frac{5 \pm 3}{2}
$$

This gives two solutions:

$$
x = \frac{5 + 3}{2} = 4 \quad \text{and} \quad x = \frac{5 - 3}{2} = 1
$$

### Conclusion

The solutions to the equation $$ x^{2} - 5x + 4 = 0 $$ are:

$$
x = 1 \quad \text{and} \quad x = 4
$$
The solutions are $$ x = 1 $$ and $$ x = 4 $$.

\( \Rightarrow \quad \partial x ^ { 2 } - 5 x + 4 = 0 \)