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

The solutions to the equation 4x^2-x-1=0 are x=(1+sqrt(17))/8 ,x=(1-sqrt(17))/8

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

The zeros of 4x^2-x-1=0 are x=(1+sqrt(17))/8 ,x=(1-sqrt(17))/8

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

x = \frac{1 + 17}{8}, x = \frac{1 - 17}{8}

Decimal Notation

x = 0.64038 \dots, x = - 0.39038 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 1)^{2} - 4 \cdot 4 (- 1) = 17

x_{1, 2} = \frac{- ( - 1 ) \pm 17}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 17}{2 \cdot 4}, x_{2} = \frac{- ( - 1 ) - 17}{2 \cdot 4}

x = \frac{- ( - 1 ) + 17}{2 \cdot 4} : \frac{1 + 17}{8}

x = \frac{- ( - 1 ) - 17}{2 \cdot 4} : \frac{1 - 17}{8}

The solutions to the quadratic equation are:

x = \frac{1 + 17}{8}, x = \frac{1 - 17}{8}

x^{2} - 14 = 2 x - 14

\frac{6 x ^{8} y ^{9}}{5 x ^{2} y ^{4}}

s^{2} + 3 s + 2 < 0

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

- x + 8 + 3 x = - 6

What are the solutions to the equation 4x^2-x-1=0 ?
The solutions to the equation 4x^2-x-1=0 are x=(1+sqrt(17))/8 ,x=(1-sqrt(17))/8
Find the zeros of 4x^2-x-1=0
The zeros of 4x^2-x-1=0 are x=(1+sqrt(17))/8 ,x=(1-sqrt(17))/8