2x^2-4x-48=0 use factorization to solve for the unknown
Wrong!!!
Look a few posts above this for a repeat of the same question, the bot
got a different wrong answer that time, lol
I answered it correctly
I apologize for the error in my previous response. Thank you for bringing it to my attention.
The correct solution to the given equation using factorization is:
2x^2 - 4x - 48 = 0
First, we can factor out a common factor of 2 from all the terms:
2(x^2 - 2x - 24) = 0
Next, we need to find two numbers that multiply to -24 and add up to -2 (the coefficient of the x term). These two numbers are -6 and 4.
So we can rewrite the expression as:
2(x - 6)(x + 4) = 0
Now, using the zero product property, we can set each factor equal to zero and solve for x:
x - 6 = 0 or x + 4 = 0
Solving for x in each equation gives us:
x = 6 or x = -4
Therefore, the solutions to the equation are x = 6 and x = -4.
To solve the quadratic equation 2x^2 - 4x - 48 = 0 using factorization, you need to find two numbers whose product is equal to (2 * -48 = -96) and whose sum is equal to (-4). Let's break down the steps:
Step 1: Set the equation equal to zero: 2x^2 - 4x - 48 = 0
Step 2: Factor out the common factor (if any): Since there is no common factor, proceed to the next step.
Step 3: Split the middle term: Look for two numbers whose product is -96 and whose sum is -4. After some trial and error, we find that -8 and 12 satisfy these conditions (-8 * 12 = -96 and -8 + 12 = -4).
Step 4: Rewrite the equation using the split middle term: 2x^2 - 8x + 12x - 48 = 0
Step 5: Group the terms and factor out the common factors in each group: (2x^2 - 8x) + (12x - 48) = 0
Step 6: Factor out the common factors within each group: 2x(x - 4) + 12(x - 4) = 0
Step 7: Factor out the common factor from both groups: (2x + 12)(x - 4) = 0
Step 8: Set each factor equal to zero and solve for x:
2x + 12 = 0 --> 2x = -12 --> x = -6
x - 4 = 0 --> x = 4
So, the solutions to the equation 2x^2 - 4x - 48 = 0 using factorization are x = -6 and x = 4.
First, we can factor out a common factor of 2, giving us:
2(x^2 - 2x - 24) = 0
Next, we need to find two numbers that multiply to -24 and add up to -2 (the coefficient of the x term). These two numbers are -6 and 4.
So we can rewrite the expression as:
2(x - 6)(x + 4) = 0
Now we can set each factor equal to zero to find the values of x that make the expression true:
x - 6 = 0 or x + 4 = 0
Solving for x in each equation gives us:
x = 6 or x = -4
So the two solutions to the equation are x = 6 and x = -4.