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

Problem

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=1

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±√(,2−4*(1)*(−1)))/(2*(1))

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

x=(−2±√(,4+4))/2

x=(−2±√(,8))/2

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

x=(−2±2√(,2))/2

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

x=−1±√(,2)

Final Answer

x=−1±√(,2)

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