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

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

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

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

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

x = \frac{1 + 2}{2}, x = \frac{1 - 2}{2}

Decimal Notation

x = 1.20710 \dots, x = - 0.20710 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 4 (- 1) = 42

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{1 + 2}{2}, x = \frac{1 - 2}{2}

lo g_{2} (2048)

\frac{- 65 x}{65} = \frac{- 390}{- 65}

(x - 2) (x - 7) < 0

3 x^{2} + 5 x - 12 = 0

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