Question

Solve the following equation by using quadratic equations for x and give your x² – 5x – 10 = 0

Answer 1

x² – 5x – 10 = 0
On comparing with, ax² + bx + c = 0
a = 1, b = -5, c = -10

∵ x = `(-b ± sqrt(b^2 - 4ac))/(2a)`

x = `(-(-5) ± sqrt((-5)^2 - 4(1)(-10)))/(2 xx 1)`

∴ x = `(5 ± sqrt(25 + 40))/(2)`

⇒ x = `(5 ± sqrt(65))/(2)`

= `(5 ± 8.06)/(2)`
Either x = `(5 + 8.06)/(2)` 

= `(13.06)/(2)`
= 6.53
or
x =`(5 - 8.06)/(2)` 

= `(-3.06)/(2)`
= 1.53
∴ x = 6.53, x = -1.53.