Question

Solve the quadratic equation 2x² – 5x – 1 = 0 for x.

Answer 1

Given: 2x² – 5x – 1 = 0

Step-wise calculation:

1. Identify coefficients:

a = 2, b = –5, c = –1

2. Use the quadratic formula

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

3. Compute the discriminant:

b² – 4ac = (–5)² – 4(2)(–1) 

= 25 + 8

= 33

4. Substitute:

`x = (5 ± sqrt(33))/4`

5. Numerical approximations:

`sqrt(33) ≈ 5.7445626465`, so

`x_1 ≈ (5 + 5.7445626465)/4 ≈ 2.6861406616`

`x_2 ≈ (5 - 5.7445626465)/4 ≈ -0.1861406616`

The solutions are `x = (5 + sqrt(33))/4 ≈ 2.68614` and `x = (5 - sqrt(33))/4 ≈ -0.18614`.