Solve Using the Quadratic Formula x^2+2x+17=0

Problem

x2+2*x+17=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=17

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)*(17)))/(2*(1))

4. Simplify the expression inside the square root, known as the discriminant.

x=(−2±√(,4−68))/2

x=(−2±√(,−64))/2

5. Apply the imaginary unit i because the discriminant is negative, where √(,−64)=8*i

x=(−2±8*i)/2

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

x=−1±4*i

Final Answer

x=−1±4*i

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