Question

Solve the following quadratic equations by factorization:

`3sqrt(5)x^2 + 25x - 10sqrt(5) = 0`

Answer 1

Given: `3sqrt(5)x^2 + 25x - 10sqrt(5) = 0`

Step-wise calculation:

1. Try to factor into two binomials:

`(sqrt(5)x + 10)(3x - sqrt(5))`

2. Expand to check:

`(sqrt(5)x)(3x) + (sqrt(5)x)(-sqrt(5)) + 10(3x) + 10(-sqrt(5))` 

= `3sqrt(5)x^2 - 5x + 30x - 10sqrt(5)`

= `3sqrt(5)x^2 + 25x - 10sqrt(5)`

3. Set each factor = 0:

`sqrt(5) x + 10 = 0`

⇒ `x = -10/sqrt(5)`

⇒ `x = -2sqrt(5)`

`3x - sqrt(5) = 0`

 ⇒ `x = sqrt(5)/3`

The solutions are `x = -2sqrt(5)` and `x = sqrt(5)/3`.