Solve Using the Quadratic Formula 3x^2-6x+1=0

Problem

3*x2−6*x+1=0

Solution

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

a=3

b=−6

c=1

2. State the quadratic formula.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−(−6)±√(,(−6)2−4*(3)*(1)))/(2*(3))

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

x=(6±√(,36−12))/6

x=(6±√(,24))/6

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

x=(6±√(,4⋅6))/6

x=(6±2√(,6))/6

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

x=(2*(3±√(,6)))/6

x=(3±√(,6))/3

Final Answer

x=(3±√(,6))/3

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