Question

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

x² – 10x + 6 = 0

Answer 1

Given: x² – 10x + 6 = 0

Step-wise calculation:

1. Identify coefficients: a = 1, b = –10, c = 6.

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

3. Compute the discriminant: b² – 4ac 

= (–10)² – 4 × 1 × 6 

= 100 – 24

= 76

4. `sqrt(76) = 8.717797886` exactly `2sqrt(19)`.

5. Apply the formula:

`x_1 = (10 + 8.717797886)/2` 

= `18.717797886/2` 

= 9.358898943

`x_2 = (10 - 8.717797886)/2` 

= `1.282202114/2` 

= 0.641101057

x = 9.36 or x = 0.64 correct to 2 decimal places.