Question

Solve the following quadratic equation: x² + 4x – 8 = 0. Give your answer correct to one decimal place.

Answer 1

Given: x² + 4x – 8 = 0

Step-wise calculation:

1. Identify coefficients: a = 1, b = 4, c = –8.

2. Quadratic formula: `x = (-b ± sqrt((b^2 - 4ac)))/(2a)`.

3. Compute discriminant: b² – 4ac 

= 4² – 4(1)(–8) 

= 16 + 32

= 48

4. `sqrt(48) = 4sqrt(3) ≈ 6.92820323`.

`x = (-4 ± 6.92820323)/2`

`x_1 = (-4 + 6.92820323)/2`

= 1.464101615...

= 1.5   ...(To 1 d.p.)

`x_2 = (-4 - 6.92820323)/2`

= –5.464101615...

= –5.5   ...(To 1 d.p.)

x = 1.5 and x = –5.5.