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

The solutions to the equation 1/2-1/2 x=-x^2+2x+1 are x=-(-5+sqrt(33))/4 ,x=(5+sqrt(33))/4

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

The zeros of 1/2-1/2 x=-x^2+2x+1 are x=-(-5+sqrt(33))/4 ,x=(5+sqrt(33))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

x = - \frac{- 5 + 33}{4}, x = \frac{5 + 33}{4}

Solution steps

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

Multiply both sides by

2

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

Switch sides

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

Move

x

to the left side

- 2 x^{2} + 5 x + 2 = 1

Move

1

to the left side

- 2 x^{2} + 5 x + 1 = 0

Solve with the quadratic formula

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

5^{2} - 4 (- 2) \cdot 1 = 33

x_{1, 2} = \frac{- 5 \pm 33}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 5 + 33}{2 ( - 2 )}, x_{2} = \frac{- 5 - 33}{2 ( - 2 )}

x = \frac{- 5 + 33}{2 ( - 2 )} : - \frac{- 5 + 33}{4}

x = \frac{- 5 - 33}{2 ( - 2 )} : \frac{5 + 33}{4}

The solutions to the quadratic equation are:

x = - \frac{- 5 + 33}{4}, x = \frac{5 + 33}{4}

5 x^{2} - 30 = 0

(- \frac{1}{3})^{0}

\frac{1}{4} + \frac{3}{2} \cdot \frac{2}{3}

- 2 - (- 3)

x^{2} + 16 x + 60 = 3 x + 20

What are the solutions to the equation 1/2-1/2 x=-x^2+2x+1 ?
The solutions to the equation 1/2-1/2 x=-x^2+2x+1 are x=-(-5+sqrt(33))/4 ,x=(5+sqrt(33))/4
Find the zeros of 1/2-1/2 x=-x^2+2x+1
The zeros of 1/2-1/2 x=-x^2+2x+1 are x=-(-5+sqrt(33))/4 ,x=(5+sqrt(33))/4