How do you solve X2 plus 24X plus 144 equals 0?

Answer 1

X^2 + 24x + 144 = 0. Dontcha just luv algebra?

You are looking for a polynomial: (X+somenumber) * (X+somenumber) = X^2 + 24x + 144.

Then just solve for (X+somenumber) * (X+somenumber) = 0.

The trick is to find the pair of factors of 144 that add up to 24.

These are the pairs of factors of 144:

1 x 144

2 x 72

3 x 48

4 x 36

6 x 24

8 x 18

12 x 12

You want the pair of factors that add up to 24:

1 + 144 = more than 144 and is too large

2 + 72 = more than 72 and is too large

3 + 48 = more than 48 and is too large

4 + 36 = more than 36 and is too large

6 + 24 = 30

8 + 18 = 26

12 + 12 = 24!

so,

(X +12) * (x + 12) = X^2 + 24 +144 = 0

So either (X +12) or the other (X +12) is going to be zero because you can only get zero from multiplying something by 0.

If X+12 =0, then put -12 on both sides of the equation:

X+12 -12 = 0 -12

x + 12-12 = -12

x + 0 = -12

x = -12.

Normally you would then solve for the other (X+12) = 0, but that's the same thing as what we just did. So this time, there is only one answer x = -12.