Solve Using the Quadratic Formula x^2+3x+4=0

Problem

x2+3*x+4=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=3

c=4

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−3±√(,3−4*(1)*(4)))/(2*(1))

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

x=(−3±√(,9−16))/2

x=(−3±√(,−7))/2

4. Express the result using the imaginary unit i since the discriminant is negative, where √(,−7)=i√(,7)

x=(−3±i√(,7))/2

Final Answer

x=(−3±i√(,7))/2

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