Solve the quadratic equation using factorisation method: b^2-b-72=0

Answer 1

To solve the quadratic equation b^2 - b - 72 = 0 using the factorization method, we need to find two numbers that multiply to give -72 and add up to -1.

Let's factorize -72:
-72 can be written as 8 * (-9) or (-8) * 9.

Next, we need to find two numbers that add up to -1 out of these two possibilities.

8 + (-9) = -1.

So, we can rewrite the equation as:
b^2 + 8b - 9b - 72 = 0.

Now, let's factor by grouping:
(b^2 + 8b) - (9b + 72) = 0.
b(b + 8) - 9(b + 8) = 0.
(b - 9)(b + 8) = 0.

According to the zero product property, either b - 9 = 0, or b + 8 = 0.

If b - 9 = 0, then b = 9.
If b + 8 = 0, then b = -8.

Therefore, the solutions to the quadratic equation b^2 - b - 72 = 0 are b = 9 and b = -8.