Solving quardratic equations using factoring.
2X^2+2X-4=0
The book says the answer is -2,1.
I got the -2,1 but not in the order of
-2,1.
I used FOIL to solve. When I use -2,1 I don't can not solve. When I use
1,-2. I can solve.
I am not clear.
The order is not important. The answer is x=-2 or x=1
Verify by substituting for x
2(-2)^2+2(-2)-4=0
8-4-4=0
0=0
2(1)^2+2(1)-4=0
2+2-4=0
0=0
To solve a quadratic equation like 2X^2 + 2X - 4 = 0 using factoring, follow these steps:
Step 1: Write down the equation in the form of ax^2 + bx + c = 0, in this case, 2X^2 + 2X - 4 = 0.
Step 2: Factor out the common factor from the terms, if possible. In this case, there is no common factor, so we proceed to the next step.
Step 3: Look for two numbers that multiply to give you the product of 'a' (the coefficient of the x^2 term) and 'c' (the constant term). In this case, 'a' is 2 and 'c' is -4, so you need to find two numbers that multiply to give you -8 (2 * -4). These numbers are 4 and -2.
Step 4: Rewrite the middle term of the quadratic equation using the two numbers you found in the previous step. Split the middle term into two terms, using the numbers 4 and -2. This is done by replacing the middle term (2X) with the sum of the two numbers (4X - 2X). So the equation becomes:
2X^2 + 4X - 2X - 4 = 0
Step 5: Group the terms and factor by grouping. Group the first two terms (2X^2 + 4X) and the last two terms (-2X - 4). Factor out the common factors from each group. In this case, the common factor in the first group is 2X, and the common factor in the second group is -2. So the equation becomes:
2X(X + 2) - 2(X + 2) = 0
Step 6: Notice that both groups have the factor (X + 2). Factor out this common factor from both terms. This results in:
(2X - 2)(X + 2) = 0
Step 7: Set each factor equal to zero and solve for X separately.
2X - 2 = 0 or X + 2 = 0
Step 8: Solve each equation:
2X = 2 or X = -2
X = 1 or X = -2
So the two solutions to the quadratic equation 2X^2 + 2X - 4 = 0 are X = 1 and X = -2.
Regarding the order of the solutions, it does not matter whether you write -2,1 or 1,-2. Both ways represent the same solutions.