Solve Using the Quadratic Formula 2x^2-4x+1=0

Problem

2*x2−4*x+1=0

Solution

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

a=2

b=−4

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=(−(−4)±√(,(−4)2−4*(2)*(1)))/(2*(2))

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

x=(4±√(,16−8))/4

x=(4±√(,8))/4

5. Simplify the radical √(,8) by factoring out the perfect square.

x=(4±2√(,2))/4

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

x=(2±√(,2))/2

Final Answer

x=(2±√(,2))/2

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