What are the solutions to the equation x*(1+x)=1 ?

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

Find the zeros of x*(1+x)=1

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x \cdot (1 + x) = 1

x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

Decimal Notation

x = 0.61803 \dots, x = - 1.61803 \dots

Solution steps

x (1 + x) = 1

Expand

x (1 + x) : x + x^{2}

x + x^{2} = 1

Move

1

to the left side

x + x^{2} - 1 = 0

Write in the standard form

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

x^{2} + x - 1 = 0

Solve with the quadratic formula

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

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

x_{1, 2} = \frac{- 1 \pm 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 1 + 5}{2 \cdot 1}, x_{2} = \frac{- 1 - 5}{2 \cdot 1}

x = \frac{- 1 + 5}{2 \cdot 1} : \frac{- 1 + 5}{2}

x = \frac{- 1 - 5}{2 \cdot 1} : \frac{- 1 - 5}{2}

The solutions to the quadratic equation are:

x = \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}

6 x^{2} - 9 x - 3 = 0

3 n - n^{2} = 0

20 = 2 + 35 t - 16 t^{2}

2 x^{2} + 16 x + 30 = 0

4 - x^{2} = 8 - 2 x^{2}

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