Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -9x2 + 4x + 7

f(x) = -9x^2 + 4x + 7 = 0

ax^2 + bx + c = 0

x = (-b ± sqrt(b^2-4*a*c)/(2*a)

from the equation

a = -9

b = 4

c = 7

x = (-b ± sqrt(b^2-4*a*c)/(2*a)

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

x = (-4 ± sqrt(16-(-252))/(-18)

x = (-4 ± sqrt(16+252))/(-18)

x = (-4 ± sqrt(268))/(-18) → sqrt(268) = 2*sqrt(67)

x = (-4 ± 2*sqrt(67))/(-18)

simplify

x = (-2 ± 1*sqrt(67))/(-9)

x = (-2 + 1*sqrt(67))/(-9) or x = (-2 - 1*sqrt(67))/(-9)

x = (2 - sqrt(67))/9 or x = (2 + sqrt(67))/9

x = -0.687 or x = 1.132