What are the solutions to the equation solvefor x,2x-x^2=0.5 ?

The solutions to the equation solvefor x,2x-x^2=0.5 are x=(2-sqrt(2))/2 ,x=(2+sqrt(2))/2

Find the zeros of solvefor x,2x-x^2=0.5

The zeros of solvefor x,2x-x^2=0.5 are x=(2-sqrt(2))/2 ,x=(2+sqrt(2))/2

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x, 2 x - x^{2} = 0.5

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

Decimal

x = 0.29289 \dots, x = 1.70710 \dots

Solution steps

2 x - x^{2} = 0.5

Multiply both sides by

10

20 x - 10 x^{2} = 5

Move

5

to the left side

20 x - 10 x^{2} - 5 = 0

Write in the standard form

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

- 10 x^{2} + 20 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 20 \pm 2 0 ^{2} - 4 ( - 10 ) ( - 5 )}{2 ( - 10 )}

2 0^{2} - 4 (- 10) (- 5) = 102

x_{1, 2} = \frac{- 20 \pm 10 2}{2 ( - 10 )}

Separate the solutions

x_{1} = \frac{- 20 + 10 2}{2 ( - 10 )}, x_{2} = \frac{- 20 - 10 2}{2 ( - 10 )}

x = \frac{- 20 + 10 2}{2 ( - 10 )} : \frac{2 - 2}{2}

x = \frac{- 20 - 10 2}{2 ( - 10 )} : \frac{2 + 2}{2}

The solutions to the quadratic equation are:

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

3 x^{2} - 9 a x^{2} - x + 3 a

(x - 3)^{2} + (x + 4)^{2} = 29

x^{2} y^{2} + x y = 6, y

a^{2} + n^{2}

2 x^{2} - 5 = 27

What are the solutions to the equation solvefor x,2x-x^2=0.5 ?
The solutions to the equation solvefor x,2x-x^2=0.5 are x=(2-sqrt(2))/2 ,x=(2+sqrt(2))/2
Find the zeros of solvefor x,2x-x^2=0.5
The zeros of solvefor x,2x-x^2=0.5 are x=(2-sqrt(2))/2 ,x=(2+sqrt(2))/2