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

Problem

2*x2−2*x−1=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=−2

c=−1

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−(−2)±√(,(−2)2−4*(2)*(−1)))/(2*(2))

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

x=(2±√(,4+8))/4

x=(2±√(,12))/4

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

x=(2±2√(,3))/4

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

x=(1±√(,3))/2

Final Answer

x=(1±√(,3))/2

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