Question

How do you solve `x^2- 3x - 28 = 0`?

Answer 1

The solutions are:
`color(blue)(x=-4 , x=7`

Explanation:

`x^2 -3x -28 = 0`

We can first factorise this expression by splitting the middle term and then find the solutions:

`=x^2 color(blue)(-7x + 4x)-28 = 0`
`=x(x-7) + 4(x-7) = 0`

`=color(blue)((x+4)(x-7)`

Now, we can equate the two factors with zero and find the solutions:

• `x+4 =0, color(blue)(x=-4`
• `x-7 =0, color(blue)(x=7`

Answer 2

Solve y = x^2 - 3x - 28 = 0

Explanation:

I use the new Transforming Method (Google, Yahoo Search). Roots have different signs (Rule of Signs).
Factor pairs of (c = -28) -> (-2, 14)(-4, 7). This sum is 3 = -b. Then the 2 real roots are: -4 and 7.

NOTE. By this method, we can avoid the lengthy factoring by grouping and solving the 2 binomials.