Question

Solve for x and give your answer correct to 2 decimal places: 

3x² – x – 7 = 0

Answer 1

Given: 3x² – x – 7 = 0

Step-wise calculation:

1. Identify coefficients: a = 3, b = –1, c = –7.

2. Use the quadratic formula `x = (-b ± sqrt((b^2 - 4ac)))/(2a)`.

3. Compute the discriminant:

Δ = b² – 4ac 

= (–1)² – 4 × 3 × (–7) 

= 1 + 84

= 85

4. `sqrt(Δ) = sqrt(85) ≈ 9.219544`.

5. `x = (-b ± sqrt(Δ))/(2a)`

= `(1 ± 9.219544)/6`

`x_1 = (1 + 9.219544)/6`

= `10.219544/6`

= 1.703257

= 1.70   ...(To 2 d.p.)

`x_2 = (1 - 9.219544)/6`

= `(-8.219544)/6`

= –1.369924

= –1.37   ...(To 2 d.p.)

x = 1.70 or x = –1.37.