Question

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

x² + 7x = 7

Answer 1

Given: x² + 7x = 7

Step-wise calculation:

1. Rearrange: x² + 7x – 7 = 0.

2. Use the quadratic formula `x = (-b ± sqrt((b^2 - 4ac)))/(2a)` with a = 1, b = 7, c = –7:

`x = (-7 ± sqrt((49 - 4 xx 1 xx (-7))))/2`

= `(-7 ± sqrt(77))/2`

3. Numerical values: `sqrt(77) ≈ 8.774964387`

`x_1 = (-7 + 8.774964387)/2`

= 0.8874821937...

= 0.89   ...(To 2 d.p.)

`x_2 = (-7 - 8.774964387)/2`

= –7.8874821937...

= –7.89   ...(To 2 d.p.)

x = 0.89 or x = –7.89 correct to 2 decimal places.