Solve by factoring 2w^2-11=-12
I'm having a super hard time with factoring....can someone plz help?
geez - impatient much?
I shall assume you mean
2x^2 - 11x = -12
2x^2 - 11x + 12 = 0
(2x-3)(x-4) = 0
x = 3/2 or 4
have the teachers taken today off????
Even teachers have their own lives, you know! Please be patient because they aren't robots!
2x^2 - 11x + 12 = 0
A*C = 2*12 = 24 = -3*-8. sum = -11 = B.
2x^2 - (3x+8x) + 12 = 0
x*(2x-3) -4(2x-3) = 0
(2x-3)(x-4) = 0
2x-3 = 0, X = 3/2.
x-4 = 0, X = 4.
Sure, I can help you solve this equation by factoring. Here's how you can do it step by step:
Step 1: Rewrite the equation in standard quadratic form, where one side is equal to zero:
2w^2 - 11 = -12
Rearrange the terms:
2w^2 + 1w - 11 + 12 = 0
2w^2 + w + 1 = 0
Step 2: Look for two numbers, let's call them a and b, such that the product of a and b is equal to the product of the coefficient of the squared term (2) and the constant term (1):
a * b = 2 * 1 = 2
Step 3: Look for two numbers, a and b, such that their sum is equal to the coefficient of the linear term (1):
a + b = 1
Step 4: Now let's find the values of a and b. This equation can be factored as follows:
2w^2 + w + 1 = 0
(a * w + 1)(b * w + 1) = 0
By comparing this equation with the original equation, we can deduce that a = 2 and b = 1/2.
So the factored form of the equation is:
(2w + 1)(w + 1/2) = 0
Step 5: Now we can set each factor equal to zero and solve for w:
2w + 1 = 0
w + 1/2 = 0
Solving the first equation:
2w = -1
w = -1/2
Solving the second equation:
w = -1/2
Step 6: The values of w that satisfy the equation 2w^2 - 11 = -12 are w = -1/2.
So, the solution to the equation is w = -1/2.