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

Problem

x2+2*x−2=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=−2

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−2±√(,2−4*(1)*(−2)))/(2*(1))

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

x=(−2±√(,4+8))/2

x=(−2±√(,12))/2

4. Simplify the radical by factoring out the largest perfect square from 12.

x=(−2±2√(,3))/2

5. Divide both terms in the numerator by the denominator to find the final values for x

x=−1±√(,3)

Final Answer

x=−1±√(,3)

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