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

Problem

2*x2−6*x+3=0

Solution

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

a=2

b=−6

c=3

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 of a b and c into the formula.

x=(−(−6)±√(,(−6)2−4*(2)*(3)))/(2*(2))

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

x=(6±√(,36−24))/4

x=(6±√(,12))/4

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

x=(6±2√(,3))/4

6. Divide the numerator and denominator by their greatest common factor, which is 2

x=(3±√(,3))/2

Final Answer

x=(3±√(,3))/2

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