Question

How do you solve `7x ^ { 2} + 37x - 30= 0`?

Answer 1

`x = 5/7 or x = -6`

Explanation:

This is a quadratic equation in the form of `ax^2+bx+c=0`.

First, you multiply `a` and `c`, in this case, `7` and `-30`, and get `-210`. Then you get factors of `ac` `(-210)` which when added give `b` `(37)`.

The factors are `42` and `-5`. You substitute this factors in place of `b`

`(7x^2+42x)(-5x-30)=0`

`7x(x+6)-5(x+6)=0`

`7x-5=0 =>x=5/7`

`x+6=0 => x=-6`

Answer 2

Solution: `x =-6 , x=5/7`

Explanation:

`7 x^2 +37 x -30 =0` or

`7 x^2 +42 x -5 x -30 =0` or

`7 x( x+6) x -5 (x +6) =0` or

`( x+6) (7 x-5) =0:.` either `x+6=0 :. x = -6.` or

`7 x - 5 =0 :. x = 5/7`

Solution: `x =-6 , x=5/7` [Ans]