Question

How do you solve `n^2-5=-4`?

Answer 1

`n=+-1`

Explanation:

To solve a quadratic equation we require to equate it to zero.

The first step is therefore to add 4 to both sides of the equation.

`rArrn^2-5+4=cancel(-4)+cancel(4)=0`

`rArrn^2-1=0" is the equation to be solved"`

Now `n^2-1` is a `color(blue)"difference of squares"`

`rArr(n-1)(n+1)=0`

solve: `n-1=0rArrn=1`

solve `n+1=0rArrn=-1`

Thus the solutions to the equation are `n=+-1`

Answer 2

`n = +-1`

Explanation:

Although this is a quadratic equation, it is a special case because there is no 'n' term.

Isolate the `n^2` term.

`n^2 = -4+5`

`n^2 = 1`

`n = +-1`