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

The solutions to the equation x^2+1/4 x-1=0 are x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8

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

The zeros of x^2+1/4 x-1=0 are x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8

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

x = \frac{- 1 + 65}{8}, x = \frac{- 1 - 65}{8}

Decimal Notation

x = 0.88278 \dots, x = - 1.13278 \dots

Solution steps

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

Multiply both sides by

4

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

Solve with the quadratic formula

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

1^{2} - 4 \cdot 4 (- 4) = 65

x_{1, 2} = \frac{- 1 \pm 65}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 1 + 65}{2 \cdot 4}, x_{2} = \frac{- 1 - 65}{2 \cdot 4}

x = \frac{- 1 + 65}{2 \cdot 4} : \frac{- 1 + 65}{8}

x = \frac{- 1 - 65}{2 \cdot 4} : \frac{- 1 - 65}{8}

The solutions to the quadratic equation are:

x = \frac{- 1 + 65}{8}, x = \frac{- 1 - 65}{8}

1 - x^{2} > 0

\frac{( 2 i )}{( 1 + i )}

- 4 k^{4} - 20 k^{3} + 24 k^{2}

\frac{3}{4} x^{2} + 7 x + 16 = 0

(- 8 x^{- 9})^{\frac{1}{3}}

What are the solutions to the equation x^2+1/4 x-1=0 ?
The solutions to the equation x^2+1/4 x-1=0 are x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8
Find the zeros of x^2+1/4 x-1=0
The zeros of x^2+1/4 x-1=0 are x=(-1+sqrt(65))/8 ,x=(-1-sqrt(65))/8