x^2 -3x - 10 = 0 ( solve the quadratic equation)

Answer 1

There are several ways to solve a quadratic equation: factoring, completing the square, and the quadratic formula are the most common. After observing the problem, factoring appears to be the simplest.

x² - 3x - 10 = 0

Let's factor the left side above. Ask yourself "What two numbers multiply to equal -10 and add to equal -3?" Since (-5)(2) = -10 and (-5) + 2 = -3, that works. So, the above equation factors to

(x - 5)(x + 2) = 0

Now that this is factors, set each factor equal to zero and solve for x:

x - 5 = 0 <--> x = 5

x + 2 = 0 <--> x = -2

Therefore our solution set is {-2, 5}.