What are the solutions to the equation a^2+4a+1=0 ?

The solutions to the equation a^2+4a+1=0 are a=-2+sqrt(3),a=-2-sqrt(3)

Find the zeros of a^2+4a+1=0

The zeros of a^2+4a+1=0 are a=-2+sqrt(3),a=-2-sqrt(3)

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

a = - 2 + 3, a = - 2 - 3

Decimal Notation

a = - 0.26794 \dots, a = - 3.73205 \dots

Solution steps

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

Solve with the quadratic formula

a_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

4^{2} - 4 \cdot 1 \cdot 1 = 23

a_{1, 2} = \frac{- 4 \pm 2 3}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- 4 + 2 3}{2 \cdot 1}, a_{2} = \frac{- 4 - 2 3}{2 \cdot 1}

a = \frac{- 4 + 2 3}{2 \cdot 1} : - 2 + 3

a = \frac{- 4 - 2 3}{2 \cdot 1} : - 2 - 3

The solutions to the quadratic equation are:

a = - 2 + 3, a = - 2 - 3

4 x^{2} - 6 x + 16 = 0

x^{2} - 14 x + 67 = 0

2 x^{2} - 4 x = 0

5 x^{2} + 5 x - 2 = 0

- 4 x^{2} + 3 x - 5 = 0

What are the solutions to the equation a^2+4a+1=0 ?
The solutions to the equation a^2+4a+1=0 are a=-2+sqrt(3),a=-2-sqrt(3)
Find the zeros of a^2+4a+1=0
The zeros of a^2+4a+1=0 are a=-2+sqrt(3),a=-2-sqrt(3)