Solve Using the Quadratic Formula 3x^2-6x+2=0

Problem

3*x2−6*x+2=0

Solution

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

a=3

b=−6

c=2

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=(−(−6)±√(,(−6)2−4*(3)*(2)))/(2*(3))

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

x=(6±√(,36−24))/6

x=(6±√(,12))/6

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

√(,12)=√(,4⋅3)=2√(,3)

x=(6±2√(,3))/6

6. Divide each term in the numerator by the denominator to find the final simplified values for x

x=6/6±(2√(,3))/6

x=1±√(,3)/3

Final Answer

x=1±√(,3)/3

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