Question

try: solve the quadratic $x^2 + 4x + 2 = 0$ by using the quadratic formula.

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 4\), \(c = 2\).

Step2: Recall quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)

Step3: Calculate discriminant

Discriminant \(D=b^2 - 4ac=(4)^2-4\times1\times2 = 16 - 8=8\)

Step4: Substitute into formula

\(x=\frac{-4\pm\sqrt{8}}{2\times1}=\frac{-4\pm2\sqrt{2}}{2}=-2\pm\sqrt{2}\)

Answer:

\(x=-2+\sqrt{2}\) or \(x=-2 - \sqrt{2}\)