What are the solutions to the equation solvefor x,x(x-1)=e ?

The solutions to the equation solvefor x,x(x-1)=e are x=(1+sqrt(1+4e))/2 ,x=(1-sqrt(1+4e))/2

Find the zeros of solvefor x,x(x-1)=e

The zeros of solvefor x,x(x-1)=e are x=(1+sqrt(1+4e))/2 ,x=(1-sqrt(1+4e))/2

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x, x (x - 1) = e

x = \frac{1 + 1 + 4 e}{2}, x = \frac{1 - 1 + 4 e}{2}

Decimal Notation

x = 2.22287 \dots, x = - 1.22287 \dots

Solution steps

x (x - 1) = e

Expand

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

x^{2} - x = e

Move

e

to the left side

x^{2} - x - e = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 1 + 4 e}{2 \cdot 1}, x_{2} = \frac{- ( - 1 ) - 1 + 4 e}{2 \cdot 1}

x = \frac{- ( - 1 ) + 1 + 4 e}{2 \cdot 1} : \frac{1 + 1 + 4 e}{2}

x = \frac{- ( - 1 ) - 1 + 4 e}{2 \cdot 1} : \frac{1 - 1 + 4 e}{2}

The solutions to the quadratic equation are:

x = \frac{1 + 1 + 4 e}{2}, x = \frac{1 - 1 + 4 e}{2}

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

\frac{3 x ^{2}}{2} = 0

5 x^{2} - 2 = 23

r^{2} = 24

x^{2} = - 7 x + 2

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