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

The solutions to the equation -x^2+1/2 x= 1/2 are x= 1/4-i(sqrt(7))/4 ,x= 1/4+i(sqrt(7))/4

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

The zeros of -x^2+1/2 x= 1/2 are x= 1/4-i(sqrt(7))/4 ,x= 1/4+i(sqrt(7))/4

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

x = \frac{1}{4} - i \frac{7}{4}, x = \frac{1}{4} + i \frac{7}{4}

Solution steps

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

Multiply both sides by

2

- 2 x^{2} + x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

x = \frac{- 1 + 7 i}{2 ( - 2 )} : \frac{1}{4} - i \frac{7}{4}

x = \frac{- 1 - 7 i}{2 ( - 2 )} : \frac{1}{4} + i \frac{7}{4}

The solutions to the quadratic equation are:

x = \frac{1}{4} - i \frac{7}{4}, x = \frac{1}{4} + i \frac{7}{4}

\frac{2 x ^{2} - 8}{5} - \frac{3 x - 9}{10} = x - 1

- x^{2} + 1 = 1

16 = (x + 7)^{2}

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

3 x^{2} - 24 x - 60 = 0

What are the solutions to the equation -x^2+1/2 x= 1/2 ?
The solutions to the equation -x^2+1/2 x= 1/2 are x= 1/4-i(sqrt(7))/4 ,x= 1/4+i(sqrt(7))/4
Find the zeros of -x^2+1/2 x= 1/2
The zeros of -x^2+1/2 x= 1/2 are x= 1/4-i(sqrt(7))/4 ,x= 1/4+i(sqrt(7))/4