Solve Using the Quadratic Formula x^2+4x+1=0

Problem

x2+4*x+1=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=1

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=(−4±√(,4−4*(1)*(1)))/(2*(1))

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

x=(−4±√(,16−4))/2

x=(−4±√(,12))/2

5. Simplify the radical by factoring out the largest perfect square.

x=(−4±2√(,3))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=−2±√(,3)

Final Answer

x=−2±√(,3)

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