how do you factor 2c^2-7c=-5? I know that you have to change it to 2c^2-7c+5=0. Then you do this: (2c )(c ). But how do I find the two numbers? I can't think of one that works..
Since 5 is a prime number, it can only be factored into 1 and 5. To add to -7, they both need to be negative. Which factor needs to be multiplied by 2 to get the sum of -7 for the middle term?
I hope this helps. Thanks for asking.
I don't think there is any factor that can be multipl;ied by 2 to get -7..
To factor the quadratic equation 2c^2 - 7c + 5 = 0, you need to find two numbers that, when multiplied, give you 2c^2 * 5 = 10c^2, and when added, give you -7c.
Here's a step-by-step process to find the factors:
1. Split the middle term: Multiply the coefficient of the quadratic term (2) and the constant term (5) to get 10. We need to find two numbers that add up to -7 and multiply to 10.
2. List all the factor pairs of 10: The factors of 10 are 1, 2, 5, and 10. We can create all possible pairs of these factors: (1, 10), (2, 5), (-1, -10), and (-2, -5).
3. Determine the correct pair: Since we want two numbers that add up to -7 and multiply to 10, we need to look for a pair whose sum is -7. In this case, the pair (-2, -5) has a sum of -7, which matches our requirement.
4. Use the two numbers to rewrite the middle term: Replace -7c with -2c - 5c in the quadratic equation.
Therefore, we can rewrite the quadratic equation as (2c - 5)(c - 1) = 0.
Now, you have successfully factored the quadratic equation 2c^2 - 7c + 5 = 0 into (2c - 5)(c - 1) = 0 using the process of finding the correct pair of numbers.