factor quadratic equation
x^2-20x-10,925
10925 = 95 * 115
(x-115)(x+95)
To factor a quadratic equation of the form "ax^2 + bx + c," start by looking for two numbers whose product is equal to "a x c" and whose sum is equal to "b."
In the given equation x^2 - 20x - 10,925, we have "a = 1," "b = -20," and "c = -10,925."
Now, we need to find two numbers that multiply to (-10,925) and add up to (-20).
The prime factorization of (-10,925) is (-5) x (-5) x (-13) x (67).
From these prime factors, we can choose two numbers, considering both positive and negative combinations, that add up to (-20).
The numbers we're looking for are "67" and "-13" since (-13) + (67) = (-20).
Next, we rewrite the quadratic equation using these two numbers:
x^2 - 13x + 67x - 10,925.
Then, we group the terms and factor them:
x(x - 13) + 67(x - 13).
Now, we notice that there is a common factor, (x - 13), which we can pull out:
(x - 13)(x + 67).
Therefore, the factored form of the quadratic equation x^2 - 20x - 10,925 is (x - 13)(x + 67).