Question

How do you solve `2x^2 - 7x - 9 = 0`?

Answer 1

I found:
`x_1=-1`
`x_2=9/2`

Explanation:

We can use the Quadratic Formula but...it is boring!
Try this instead:
Divide by `2`:
`x^2-7/2x-9/2=0`
Rearrange:
`x^2-7/2x=9/2`
Add ans subtract `49/16`;
`x^2-7/2x+49/16-49/16=9/2`
Rearrange:
`x^2-7/2x+49/16=9/2+49/16`
`(x-7/4)^2=(72+49)/16=121/16`
`x-7/4=+-sqrt(121/16)=+-11/4`
So:
`x_1=7/4-11/4=-1`
`x_2=7/4+11/4=-18/4=9/2`

Answer 2

Solve `y = 2x^2 - 7x - 9 = 0`

Explanation:

To solve this type of quadratic equation, use shortcut. It can save you a lot of time and work.
(a - b + c = 0) --> 2 real roots: x = - 1, and `x = -c/a = 9/2`

Remind of Shortcut:

1. When (a + b + c = 0) -> 2 real roots: 1 and `(c/a)`

2. When (a - b + c = 0 -> 2 real roots: - 1 and `(-c/a)`