solve 2z^2=5z+3 by factoring. I'm supposed to use ax^2+bx+c=0, but I don't know hot to make it so that they're all on one side and still aren't negatives. Please help.
2z^2 -5z -3 = 0
(2z +1)(z -3) = 0
z = -1/2 or z = 3
2z^2 = 5z + 3
Move them all to one side by subtracting 5z + 3 from both sides.
2z^2 - 5z - 3 = 0
I think I understand why you are confused. ax^2+bx+c = 0 is the general form of a quadratic equation.
In this case..
a = 2
b = -5
c = -3
Substitute the values into the general quadratic equation.
2x^2 + (-5)x + (-3) = 0
which is the same as
2x^2 - 5x - 3 = 0
You can change x to z.
2z^2 - 5x - 3 = 0
Now, factor it.
thanks! :D
To solve the quadratic equation 2z^2 = 5z + 3 by factoring, you need to rearrange the equation in the form of ax^2 + bx + c = 0. Here's how you can do it:
1. Start with the given equation: 2z^2 = 5z + 3.
2. Subtract 5z and 3 from both sides of the equation to move all terms to the left side: 2z^2 - 5z - 3 = 0.
3. Now, the equation is in the desired form: ax^2 + bx + c = 0. In this case, a = 2, b = -5, and c = -3.
To factor the quadratic equation, follow these steps:
1. Write down two pairs of parentheses: ( )( ).
2. Since a = 2, the first term in each parentheses must be 2z. So, write (2z )( ).
3. Now, find two numbers that multiply to give -3 (the last term, c) and add up to give -5 (the middle term, b). In this case, the numbers are -3 and +1.
4. Insert -3z and +1z into the parentheses, (2z - 3)(z + 1).
5. Now you have factored the equation: (2z - 3)(z + 1) = 0.
To find the solutions, set each factor equal to zero and solve for z:
2z - 3 = 0, which gives z = 3/2.
z + 1 = 0, which gives z = -1.
So, the solutions to the equation 2z^2 = 5z + 3 are z = 3/2 and z = -1.