Solve using the quadratic formula.

5z2 + 9z − 7 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

z =
or z =

1 answer

Using the quadratic formula: z = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values from the equation 5z2 + 9z − 7 = 0:

a = 5, b = 9, c = -7

z = (-9 ± √(9^2 - 4*5*(-7))) / (2*5)
z = (-9 ± √(81 + 140)) / 10
z = (-9 ± √221) / 10

Therefore, z = (-9 + √221) / 10 or z = (-9 - √221) / 10

These are the exact solutions. If we want decimal approximations, z ≈ 0.63 or z ≈ -2.23.