What are the solutions to the equation 2x(2x-1)=x-1 ?

The solutions to the equation 2x(2x-1)=x-1 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8

Find the zeros of 2x(2x-1)=x-1

The zeros of 2x(2x-1)=x-1 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8

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

x = \frac{3}{8} + i \frac{7}{8}, x = \frac{3}{8} - i \frac{7}{8}

Solution steps

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

Expand

2 x (2 x - 1) : 4 x^{2} - 2 x

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

Move

1

to the left side

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

Move

x

to the left side

4 x^{2} - 3 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 4 \cdot 1}{2 \cdot 4}

Simplify

(- 3)^{2} - 4 \cdot 4 \cdot 1 : 7 i

x_{1, 2} = \frac{- ( - 3 ) \pm 7 i}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 7 i}{2 \cdot 4}, x_{2} = \frac{- ( - 3 ) - 7 i}{2 \cdot 4}

x = \frac{- ( - 3 ) + 7 i}{2 \cdot 4} : \frac{3}{8} + i \frac{7}{8}

x = \frac{- ( - 3 ) - 7 i}{2 \cdot 4} : \frac{3}{8} - i \frac{7}{8}

The solutions to the quadratic equation are:

x = \frac{3}{8} + i \frac{7}{8}, x = \frac{3}{8} - i \frac{7}{8}

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

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

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

m^{2} - 4 m + 4 = 8

x^{2} + 5 x - 225 = 0

What are the solutions to the equation 2x(2x-1)=x-1 ?
The solutions to the equation 2x(2x-1)=x-1 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8
Find the zeros of 2x(2x-1)=x-1
The zeros of 2x(2x-1)=x-1 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8