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

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

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

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

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x (x + 1) = 1

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

Decimal Notation

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

Solution steps

x (x + 1) = 1

Expand

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

x^{2} + x = 1

Move

1

to the left side

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}

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

9 x^{2} - 24 x + 17 = 0

2 x^{2} + 21 x - 11 = 0

6 x^{2} - 12 x = 3

12 x^{2} + 12 x + 3 = 0

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