Solve x ^ 2 + 4x + 1 = 0

Evaluate

x^{2} + 4 x + 1 = 0

Substitute a= 1,b= 4 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 4 \pm 4 ^{2} - 4}{2}

Simplify the expression

More Steps

x = \frac{- 4 \pm 12}{2}

Simplify the radical expression

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x = \frac{- 4 \pm 2 3}{2}

Separate the equation into 2 possible cases

x = \frac{- 4 + 2 3}{2} x = \frac{- 4 - 2 3}{2}

Simplify the expression

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x = - 2 + 3 x = \frac{- 4 - 2 3}{2}

Simplify the expression

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x = - 2 + 3 x = - 2 - 3

Solution

x_{1} = - 2 - 3, x_{2} = - 2 + 3

Alternative Form

x_{1} \approx - 3.732051, x_{2} \approx - 0.267949

Solve the quadratic equation