Find the solution to 36z^2+96z+15=0
divide the original answer by 3
and get
12Z^2 + 32Z + 5 = 0
now find common factor of 12, that work for the equation
(6Z + 1)(2Z +5)=0
6Z = -1
z= -1/6
2Z = -5
Z= -5/2
now plug each Z value in to the equation (one at a time) and see which Z value lets the equation equal to zero.
this answer is wrong, the answer would be -5/2, -1/6
To find the solution to the quadratic equation 36z^2 + 96z + 15 = 0, we can use the quadratic formula. The quadratic formula is given by:
z = (-b ± √(b^2 - 4ac)) / (2a)
In the given equation, the coefficients are:
a = 36
b = 96
c = 15
We can substitute these values into the quadratic formula to find the solutions for z.
z = (-(96) ± √((96)^2 - 4(36)(15))) / (2(36))
Now let's simplify the equation step by step:
z = (-96 ± √(9216 - 2160)) / (72)
z = (-96 ± √(7056)) / (72)
z = (-96 ± 84) / (72)
Now, let's solve for both possible values of z:
Solving for the positive square root:
z = (-96 + 84) / 72
z = -12 / 72
z = -1/6
Solving for the negative square root:
z = (-96 - 84) / 72
z = -180 / 72
z = -5/2
Therefore, the solutions to the quadratic equation 36z^2 + 96z + 15 = 0 are z = -1/6 and z = -5/2.