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

Problem

3*x2+2*x+1=0

Solution

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

a=3

b=2

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 values of a b and c into the formula.

x=(−(2)±√(,(2)2−4*(3)*(1)))/(2*(3))

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

x=(−2±√(,4−12))/6

x=(−2±√(,−8))/6

5. Simplify the radical using the imaginary unit i where √(,−1)=i

√(,−8)=√(,4⋅2⋅−1)=2*i√(,2)

x=(−2±2*i√(,2))/6

6. Reduce the fraction by dividing the numerator and the denominator by their greatest common factor, which is 2

x=(2*(−1±i√(,2)))/6

x=(−1±i√(,2))/3

Final Answer

x=(−1±i√(,2))/3

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