2x^2-46x-48=0 use factorization to solve for the unknown
As simple as this:
(besides that, the bot got it wrong again)
2x^2-46x-48=0 , divide each term by 2
x^2 - 23x - 24 = 0
(x - 24)(x + 1) = 0
x = 24 or x = -1
I apologize for the mistake in my earlier response. Thank you for providing the correct solution. Yes, you can divide each term by 2 to simplify the quadratic equation. The factorization of x^2 - 23x - 24 = 0 is (x-24)(x+1) = 0, which gives the solutions x = 24 and x = -1. Thank you for bringing this to my attention.
To solve the equation 2x^2 - 46x - 48 = 0 using factorization, follow these steps:
Step 1: Factor out the common factor, if possible.
In this equation, there is no common factor that can be factored out.
Step 2: Find two numbers that multiply to give you the product of the coefficient of x^2 (in this case, 2) and the constant term (in this case, -48), and add up to give you the coefficient of x (in this case, -46).
The product of 2 and -48 is -96. The numbers whose product is -96 and whose sum is -46 are -48 and +2.
Step 3: Rewrite the middle term (-46x) using the two numbers found in Step 2.
Replace -46x with -48x + 2x.
The equation now becomes: 2x^2 - 48x + 2x - 48 = 0.
Step 4: Group the terms and factor by grouping.
Factor out the greatest common factor from the first two terms and from the last two terms.
The equation becomes: 2x(x - 24) + 2(x - 24) = 0.
Step 5: Factor out the common binomial expression (x - 24).
The equation now becomes: (x - 24)(2x + 2) = 0.
Step 6: Set each factor equal to zero and solve for x.
(x - 24) = 0 or (2x + 2) = 0.
By solving these equations, you get two possible solutions:
x = 24 or x = -1.
Therefore, the solution to the equation 2x^2 - 46x - 48 = 0 using factorization is x = 24 or x = -1.
To factorize the quadratic equation 2x^2-46x-48=0, we first need to find two numbers that multiply to give -96 and add to give -46. These numbers are -2 and 24.
We can then rewrite the equation as:
2x^2 - 2x + 24x - 48 = 0
We can now group the terms and factorize by taking out the common factors:
2x(x-1) + 24(x-1) = 0
Factorizing further, we get:
(2x+24)(x-1) = 0
Setting each factor to zero gives the two solutions:
2x + 24 = 0 or x-1 = 0
Solving for x, we get:
x = -12 or x = 1
Therefore, the solutions to the original quadratic equation are x = -12 and x = 1.