What are the solutions to the equation x^2-x=e ?

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

Find the zeros of x^2-x=e

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

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x^{2} - x = 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^{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}

2 c^{2} - 4 c = 4

x^{2} + 4 x = 12

x^{2} + 18 x - 111 = 0

3 x (4 x + 5) = 7 (4 x + 5)

w^{2} - 25 = 0

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