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

Problem

x2+2*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=2

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 values of a b and c into the formula.

x=(−2±√(,2−4*(1)*(5)))/(2*(1))

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

x=(−2±√(,4−20))/2

x=(−2±√(,−16))/2

5. Apply the imaginary unit i to handle the square root of the negative number, where √(,−16)=4*i

x=(−2±4*i)/2

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

x=−1±2*i

Final Answer

x2+2*x+5=0⇒x=−1±2*i

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