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

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

Find the zeros of 1/4 x^2+x+1/4 =0

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

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

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

Decimal Notation

x = - 0.26794 \dots, x = - 3.73205 \dots

Solution steps

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

Multiply both sides by

4

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

- 3 x^{2} - 2 x = 2

(x + 1) (x - 4) = 0

20 - 2 (- 8 + 5)

3 x + 7 = 4 x - 3

- 2 = \frac{3 x}{5} + 1

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