Ok, I am supposed to find out what the variables are by factoring and finding square roots. I couldn't find the right factors of a and c that added up to b in the equation (did that make sense?). Please help me find them! TYVM
-5n+6n^2-4=0
6y^2+12y+13=2y^2+4 simplified is:
4y^2+12y+9=0.
I know the answer to the second equation is -3/2, so I know it is a binomial square we are dealing with. Plz help, any help is greatly appreciated!
-5n+6n^2-4=0 or
6n^2-5n-4=0 does it factor to
(3n -4)(2n+ 1)
4y^2+12y+9=0.
(2y+3)^2
The first equation is -5n+6n^2-4, not 6n^2-5n-4=0. Thnx for all your help!!
the roots of the equation are
n=[(-b)+sqrt(b^2-4*a*c)]/2*a
n=[(-b)-sqrt(b^2-4*a*c)]/2*a
thus,
n=[5+sqrt(25+96)]/2*6
n=[5-sqrt(25+96)]/2*6
so,the values of n for this eqn. are
n=4/3,-1/2
To find the factors and solve the equations, let's walk through the steps together.
For the equation -5n+6n^2-4=0, we need to factorize it.
-5n + 6n^2 - 4 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to give us 6 (-5 * -4) and add up to give us -5.
Upon inspection, we can see that -1 and -4 are the factors we need:
-1 * -4 = 4
-1 + (-4) = -5
So we can rewrite the equation as:
-5n + 6n^2 - 4 = 0
-5n - 4 + 6n^2 = 0
Rearranging the terms, we have:
6n^2 - 5n - 4 = 0
Now, we can factorize this equation by breaking down the middle term (-5n) using the factors of the leading coefficient (6) and the constant term (-4).
The factors of 6 are: 1, 2, 3, 6
The factors of -4 are: -1, -2, -4
We need to find the right combination of factors that will give us -5n when added. After trying different combinations, we find that the factors -3n and 2n can be used:
(3n - 4)(2n + 1) = 0
So the factored form of the equation is (3n - 4)(2n + 1) = 0.
Moving on to the second equation, 4y^2 + 12y + 9 = 0, you correctly observed that it is a perfect square trinomial since it can be simplified to (2y + 3)^2 = 0.
Taking the square root of both sides, we get:
2y + 3 = 0
Solving for y, we have:
2y = -3
y = -3/2
Therefore, the solution to the equation 4y^2 + 12y + 9 = 0 is y = -3/2.
In conclusion:
- The factored form of the equation -5n + 6n^2 - 4 = 0 is (3n - 4)(2n + 1) = 0.
- The solution to the equation 4y^2 + 12y + 9 = 0 is y = -3/2.
I hope this explanation helps! Let me know if you have any further questions.