What is the solution to the following equation?

Question

`x^{2}-9x+18=0` show all steps

Answer 1

We can solve this equation by factoring or by using the quadratic formula.

Let's first try factoring.

We are looking for two numbers whose product is 18 and whose sum is -9. The numbers -3 and -6 satisfy this condition, since -3 * -6 = 18 and -3 + (-6) = -9.
Therefore, we can write the equation as:

(x - 3)(x - 6) = 0

Now, we can set each factor equal to zero and solve for x:

x - 3 = 0 or x - 6 = 0

Solving each equation separately:

For x - 3 = 0,
x = 3

For x - 6 = 0,
x = 6

So the solutions to the equation x^2 - 9x + 18 = 0 are x = 3 and x = 6.