Question

Solve the following equation using quadratic formula:

25x² + 30x + 7 = 0

Answer 1

Comparing equation 25x² + 30x + 7 = 0 with ax² + bx + c = 0, we get:

a = 25, b = 30 and c = 7

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(30) ± sqrt((30)^2 - 4 xx 25 xx 7))/(2(25))`

= `(-30 ± sqrt(900 - 700))/50`

= `(-30 ± sqrt(200))/50`

= `(-30 ± sqrt(2 xx 100))/50`

= `(-30 ± 10sqrt(2))/50`

= `(10(-3 ± sqrt(2)))/50`

= `((-3 ± sqrt(2)))/5`

= `((-3 ± sqrt(2)))/5` or `((-3 - sqrt(2)))/5`

Hence, `x = {(-3 + sqrt(2))/5, (-3 - sqrt(2))/5}`.