Factor x^2-48x-48=0
you have to think of two numbers that multiply to equal -48 and add to be -48
I can't think of anything that will work here.
-48 = -24 times 2 or -2 times 24
= -48 times 1 or -1 times 48
Do you have a typo?
To factor the quadratic equation x^2 - 48x - 48 = 0, we need to find two numbers whose product is -48 and whose sum is -48.
Let's break down the steps to find the factors:
Step 1: Multiply the coefficient of the x^2 term and the constant term. In this case, (-48) * (-48) = 2304.
Step 2: Find two numbers whose product is 2304 and whose sum is (-48). To do this, we can try different combinations of factors of 2304 until we find the pair that satisfies the sum condition.
Factors of 2304: 1, 2, 3, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 768, 1152, 2304
After trying several combinations, we can see that 48 and -48 are the numbers whose product is 2304 and the sum is -48.
Step 3: Now we replace the coefficient of the x term (-48x) with its factors, 48 and -48. This gives us the quadratic equation:
x^2 + 48x - 48x - 48 = 0
Step 4: Now, we group the terms and factor by grouping:
(x^2 + 48x) + (-48) = 0
x(x + 48) - 1(48) = 0
Step 5: Finally, we can factor out the common term from each group:
x(x + 48) - 1(48) = 0
x(x + 48) - 48 = 0
Now the quadratic equation is factored as (x - 1)(x + 48) = 0, so the solutions are x = 1 and x = -48.