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

The solutions to the equation (2x-1)^2=4x are x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2

Find the zeros of (2x-1)^2=4x

The zeros of (2x-1)^2=4x are x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2

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

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

Decimal Notation

x = 1.86602 \dots, x = 0.13397 \dots

Solution steps

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

Expand

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

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

Move

4 x

to the left side

4 x^{2} - 8 x + 1 = 0

Solve with the quadratic formula

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

(- 8)^{2} - 4 \cdot 4 \cdot 1 = 43

x_{1, 2} = \frac{- ( - 8 ) \pm 4 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 3}{2 \cdot 4}, x_{2} = \frac{- ( - 8 ) - 4 3}{2 \cdot 4}

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

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

The solutions to the quadratic equation are:

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

- 5 x^{2} = 90 x + 360

3 r^{2} - 2 r = 21

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

y (4 y + 1) = 8

5 x^{2} - 100 = 25

What are the solutions to the equation (2x-1)^2=4x ?
The solutions to the equation (2x-1)^2=4x are x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2
Find the zeros of (2x-1)^2=4x
The zeros of (2x-1)^2=4x are x=(2+sqrt(3))/2 ,x=(2-sqrt(3))/2