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

Problem

2*x2−3*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=−3

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=(−(−3)±√(,(−3)2−4*(2)*(1)))/(2*(2))

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

x=(3±√(,9−8))/4

x=(3±√(,1))/4

5. Evaluate the square root and solve for both possible values of x

x=(3±1)/4

6. Calculate the first solution using the plus sign.

x=(3+1)/4=4/4=1

7. Calculate the second solution using the minus sign.

x=(3−1)/4=2/4=1/2

Final Answer

x=1,1/2

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