Solve the equation.

Question

x^2-14x+48=0

Answer 1

To solve the equation x^2 - 14x + 48 = 0, we can factorize it by finding two numbers that multiply to 48 and add up to -14.

The factor pairs of 48 are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).

Looking at these pairs, we find that -6 and -8 add up to -14 and multiply to 48.

So, we can factorize the equation as (x - 6)(x - 8) = 0.

Setting each factor equal to zero, we have:

x - 6 = 0 or x - 8 = 0

Solving each of these equations separately:

x - 6 = 0
Adding 6 to both sides: x = 6

x - 8 = 0
Adding 8 to both sides: x = 8

Therefore, the solutions to the equation x^2 - 14x + 48 = 0 are x = 6 and x = 8.