What are the solutions to the equation 2xx+1=2x-1x ?

The solutions to the equation 2xx+1=2x-1x are x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4

Find the zeros of 2xx+1=2x-1x

The zeros of 2xx+1=2x-1x are x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4

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2 xx + 1 = 2 x - 1 x

x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

Solution steps

2 xx + 1 = 2 x - 1 \cdot x

Expand

2 xx + 1 : 2 x^{2} + 1

2 x^{2} + 1 = x

Move

x

to the left side

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

Write in the standard form

a x^{2} + b x + c = 0

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

Solve with the quadratic formula

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

Simplify

(- 1)^{2} - 4 \cdot 2 \cdot 1 : 7 i

x_{1, 2} = \frac{- ( - 1 ) \pm 7 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 7 i}{2 \cdot 2}, x_{2} = \frac{- ( - 1 ) - 7 i}{2 \cdot 2}

x = \frac{- ( - 1 ) + 7 i}{2 \cdot 2} : \frac{1}{4} + i \frac{7}{4}

x = \frac{- ( - 1 ) - 7 i}{2 \cdot 2} : \frac{1}{4} - i \frac{7}{4}

The solutions to the quadratic equation are:

x = \frac{1}{4} + i \frac{7}{4}, x = \frac{1}{4} - i \frac{7}{4}

y, x = 2 y^{2} - 4

2 x (2 x - 1) = x - 1

5 x^{2} - 30 x + 0 = 0

(x)^{2} + (x + 2)^{2} = 100

2 x (x - 5) = 5 x + 1

What are the solutions to the equation 2xx+1=2x-1x ?
The solutions to the equation 2xx+1=2x-1x are x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4
Find the zeros of 2xx+1=2x-1x
The zeros of 2xx+1=2x-1x are x= 1/4+i(sqrt(7))/4 ,x= 1/4-i(sqrt(7))/4