Solve the equation for real solutions by the quadratic formula.

Question

9x2−5x−7=0

Answer 1

To solve the equation 9x^2 - 5x - 7 = 0 using the quadratic formula, we first identify the coefficients of the variables:

a = 9
b = -5
c = -7

Then, we substitute these values into the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Plugging in the values, we get:

x = (-(-5) ± sqrt((-5)^2 - 4(9)(-7))) / (2(9))

Simplifying further:

x = (5 ± sqrt(25 + 252)) / 18

x = (5 ± sqrt(277)) / 18

Therefore, the real solutions to the equation 9x^2 - 5x - 7 = 0 are:

x = (5 + sqrt(277)) / 18
x = (5 - sqrt(277)) / 18