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

The solutions to the equation x= 1/2 x^2-1/2 x+1 are x=2,x=1

Find the zeros of x= 1/2 x^2-1/2 x+1

The zeros of x= 1/2 x^2-1/2 x+1 are x=2,x=1

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x = \frac{1}{2} x^{2} - \frac{1}{2} x + 1

x = 2, x = 1

Solution steps

x = \frac{1}{2} x^{2} - \frac{1}{2} x + 1

Multiply both sides by

2

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

Switch sides

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

Move

2 x

to the left side

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 1 \cdot 2 = 1

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

Separate the solutions

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

x = \frac{- ( - 3 ) + 1}{2 \cdot 1} : 2

x = \frac{- ( - 3 ) - 1}{2 \cdot 1} : 1

The solutions to the quadratic equation are:

x = 2, x = 1

m^{2} + 18 = 0

\frac{x ^{2}}{16} + 5 = 10

- 4 x^{2} + 8000 x = 1000000

0.1 x^{2} - 30 x + 2250 = 0

x^{2} + 10 = 1

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