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

Problem

x2−2*x+2=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0

a=1

b=−2

c=2

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*(1)*(2)))/(2*(1))

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

x=(2±√(,4−8))/2

x=(2±√(,−4))/2

5. Evaluate the square root of the negative number using the imaginary unit i where √(,−1)=i

x=(2±2*i)/2

6. Divide each term in the numerator by the denominator to find the final solutions.

x=1±i

Final Answer

x=1±i

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