Solve the following equation and calculate the answer correct to two decimal places :
`x^(2)-5x-10=0`.

Answer

To solve the equation \( x^2 - 5x - 10 = 0 \), we will use the quadratic formula, which is given by:

\[ x = \frac{-b \pm \sqrt{d}}{2a} \]

where \( d = b^2 - 4ac \).

### Step 1: Identify coefficients
In the equation \( x^2 - 5x - 10 = 0 \):
- \( a = 1 \)
- \( b = -5 \)
- \( c = -10 \)

### Step 2: Calculate the discriminant \( d \)
Using the formula for the discriminant:

\[ d = b^2 - 4ac \]

Substituting the values of \( a \), \( b \), and \( c \):

\[ d = (-5)^2 - 4 \cdot 1 \cdot (-10) \]
\[ d = 25 + 40 \]
\[ d = 65 \]

### Step 3: Calculate the square root of the discriminant
Now, we find \( \sqrt{d} \):

\[ \sqrt{d} = \sqrt{65} \approx 8.06 \quad (\text{to two decimal places}) \]

### Step 4: Substitute values into the quadratic formula
Now we can substitute \( b \) and \( \sqrt{d} \) into the quadratic formula:

\[ x = \frac{-(-5) \pm \sqrt{65}}{2 \cdot 1} \]
\[ x = \frac{5 \pm 8.06}{2} \]

### Step 5: Calculate the two possible values for \( x \)
1. First value:

\[ x_1 = \frac{5 + 8.06}{2} = \frac{13.06}{2} \approx 6.53 \]

2. Second value:

\[ x_2 = \frac{5 - 8.06}{2} = \frac{-3.06}{2} \approx -1.53 \]

### Final Answer
Thus, the two solutions to the equation \( x^2 - 5x - 10 = 0 \) are:

\[ x_1 \approx 6.53 \quad \text{and} \quad x_2 \approx -1.53 \]