Question

Gabby solved x^2 - 3x = 4 as shown below:

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = -4 and x = 1

Caitlyn says Gabby is wrong and believes this is the solution:

x2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = 4 and x = -1

Is Gabby or Caitlyn correct? What mistake was made by the incorrect girl?

Answer 1

Caitlyn is correct here, When you are down to

\[\large (x - 4)(x + 1)=0\]

you find out when that equation equals 0

Since 2 thing are being multiplied, we know that is either one is 0...anything multiplied by it will still equate to 0

So that means..either

(x - 4) will equal 0
or
(x + 1) will equal 0

When does that happen in both cases? Well

(x - 4) = 0 happens when x = 4
and
(x + 1) = 0 when x = -1