Solve Using the Quadratic Formula x^2+4x+5=0

Problem

x2+4*x+5=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=4

c=5

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the identified values into the quadratic formula.

x=(−4±√(,4−4*(1)*(5)))/(2*(1))

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

x=(−4±√(,16−20))/2

x=(−4±√(,−4))/2

5. Apply the definition of the imaginary unit i=√(,−1) to simplify the square root of the negative number.

x=(−4±2*i)/2

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

x=−2±i

Final Answer

x=−2±i

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