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

Problem

x2+2*x+3=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=3

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)*(3)))/(2*(1))

4. Simplify the expression inside the square root, which is the discriminant.

x=(−2±√(,4−12))/2

x=(−2±√(,−8))/2

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

√(,−8)=√(,4⋅2⋅−1)

√(,−8)=2*i√(,2)

6. Substitute the simplified radical back into the expression for x

x=(−2±2*i√(,2))/2

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

x=−1±i√(,2)

Final Answer

x=−1±i√(,2)

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