Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth.

2a^2- 30a+ 108= 0

1 answer

To solve the quadratic equation 2a^2 - 30a + 108 = 0, we can use the quadratic formula which gives us:

a = (-b ± √(b^2 - 4ac)) / 2a

In this case:
a = -30 (the coefficient of a)
b = 30 (the coefficient of a with a negative sign)
c = 108

Inserting these values into the quadratic formula, we have:

a = (-(-30) ± √((-30)^2 - 4(2)(108))) / (2(2))

Simplifying further:

a = (30 ± √(900 - 864)) / 4
a = (30 ± √36) / 4
a = (30 ± 6) / 4

This gives us two possible solutions:
a = (30 + 6) / 4 ≈ 9
or
a = (30 - 6) / 4 ≈ 6

Therefore, the solutions to the equation 2a^2 - 30a + 108 = 0 are approximately a = 9 and a = 6.