What are the solutions to the equation 4b^2-8b-1=0 ?

The solutions to the equation 4b^2-8b-1=0 are b=(2+sqrt(5))/2 ,b=(2-sqrt(5))/2

Find the zeros of 4b^2-8b-1=0

The zeros of 4b^2-8b-1=0 are b=(2+sqrt(5))/2 ,b=(2-sqrt(5))/2

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4 b^{2} - 8 b - 1 = 0

b = \frac{2 + 5}{2}, b = \frac{2 - 5}{2}

Decimal Notation

b = 2.11803 \dots, b = - 0.11803 \dots

Solution steps

4 b^{2} - 8 b - 1 = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 4 ( - 1 )}{2 \cdot 4}

(- 8)^{2} - 4 \cdot 4 (- 1) = 45

b_{1, 2} = \frac{- ( - 8 ) \pm 4 5}{2 \cdot 4}

Separate the solutions

b_{1} = \frac{- ( - 8 ) + 4 5}{2 \cdot 4}, b_{2} = \frac{- ( - 8 ) - 4 5}{2 \cdot 4}

b = \frac{- ( - 8 ) + 4 5}{2 \cdot 4} : \frac{2 + 5}{2}

b = \frac{- ( - 8 ) - 4 5}{2 \cdot 4} : \frac{2 - 5}{2}

The solutions to the quadratic equation are:

b = \frac{2 + 5}{2}, b = \frac{2 - 5}{2}

lo g_{2} (12) - 2 lo g_{2} (x)

2 y + 18 = 12 - 6 (y + 7)

30 m^{2} + 66 m + 36

2 x^{2} + 6

24 - 6 n = 54

What are the solutions to the equation 4b^2-8b-1=0 ?
The solutions to the equation 4b^2-8b-1=0 are b=(2+sqrt(5))/2 ,b=(2-sqrt(5))/2
Find the zeros of 4b^2-8b-1=0
The zeros of 4b^2-8b-1=0 are b=(2+sqrt(5))/2 ,b=(2-sqrt(5))/2