What are the solutions to the equation (2x-3)^2=2x-x^2 ?

The solutions to the equation (2x-3)^2=2x-x^2 are x= 9/5 ,x=1

Find the zeros of (2x-3)^2=2x-x^2

The zeros of (2x-3)^2=2x-x^2 are x= 9/5 ,x=1

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(2 x - 3)^{2} = 2 x - x^{2}

x = \frac{9}{5}, x = 1

Decimal Notation

x = 1.8, x = 1

Solution steps

(2 x - 3)^{2} = 2 x - x^{2}

Expand

(2 x - 3)^{2} : 4 x^{2} - 12 x + 9

4 x^{2} - 12 x + 9 = 2 x - x^{2}

Move

x^{2}

to the left side

5 x^{2} - 12 x + 9 = 2 x

Move

2 x

to the left side

5 x^{2} - 14 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 5 \cdot 9}{2 \cdot 5}

(- 14)^{2} - 4 \cdot 5 \cdot 9 = 4

x_{1, 2} = \frac{- ( - 14 ) \pm 4}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 14 ) + 4}{2 \cdot 5}, x_{2} = \frac{- ( - 14 ) - 4}{2 \cdot 5}

x = \frac{- ( - 14 ) + 4}{2 \cdot 5} : \frac{9}{5}

x = \frac{- ( - 14 ) - 4}{2 \cdot 5} : 1

The solutions to the quadratic equation are:

x = \frac{9}{5}, x = 1

- 6 x^{2} - 24 x + 1 = 13

- 3 x^{2} - 12 x + 9 = 0

2 x^{2} = 3 - 8 x

4 x^{2} - 13 x = 56

x, x^{2} + k x + x = 8 + k

What are the solutions to the equation (2x-3)^2=2x-x^2 ?
The solutions to the equation (2x-3)^2=2x-x^2 are x= 9/5 ,x=1
Find the zeros of (2x-3)^2=2x-x^2
The zeros of (2x-3)^2=2x-x^2 are x= 9/5 ,x=1