Question

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

x² – 7x + 3 = 0

Answer 1

Given: x² – 7x + 3 = 0

Step-wise calculation:

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

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

3. Discriminant: D = b² – 4ac

= (–7)² – 4(1)(3) 

= 49 – 12

= 37

4. `sqrt(D) = sqrt(37) ≈ 6.08276253`.

`x_1 = (7 + 6.08276253)/2`

= `13.08276253/2`

= 6.54138127 

= 6.54   ...(To 2 d.p.)

`x_2 = (7 - 6.08276253)/2`

= `0.91723747/2`

= 0.45861874

= 0.46   ...(To 2 d.p.)

`x = (7 ± sqrt(37))/2`

So, x = 6.54 or x = 0.46 correct to 2 decimal places.