To solve the quadratic equation 9x² = 4, we first rearrange the equation to set it to zero:
9x² – 4 = 0
This is a standard quadratic form, which we can solve using the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, we have:
- a = 9
- b = 0
- c = -4
Now we compute the discriminant (b² – 4ac):
Discriminant = 0² – 4(9)(-4) = 0 + 144 = 144
Since the discriminant is positive, we will get two real solutions. Let’s substitute into the quadratic formula:
x = (-0 ± √144) / (2 * 9)
This simplifies to:
x = (±12) / 18
Thus, we have:
x = 12 / 18 = 2/3 and x = -12 / 18 = -2/3
So the solutions to the equation 9x² = 4 are:
x = 2/3 and x = -2/3.