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

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1 Answer

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