Solve Using the Quadratic Formula 9x^2+3x-1=0

Problem

9*x2+3*x−1=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=9

b=3

c=−1

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−(3)±√(,(3)2−4*(9)*(−1)))/(2*(9))

4. Simplify the expression inside the square root (the discriminant).

x=(−3±√(,9+36))/18

x=(−3±√(,45))/18

5. Simplify the radical by factoring out the largest perfect square.

√(,45)=√(,9⋅5)=3√(,5)

x=(−3±3√(,5))/18

6. Factor out the common factor of 3 in the numerator and divide.

x=(3*(−1±√(,5)))/18

x=(−1±√(,5))/6

Final Answer

x=(−1±√(,5))/6

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