What are the solutions to the equation 4+2x-x^2=-1/2 x ?

The solutions to the equation 4+2x-x^2=-1/2 x are x=-(-5+sqrt(89))/4 ,x=(5+sqrt(89))/4

Find the zeros of 4+2x-x^2=-1/2 x

The zeros of 4+2x-x^2=-1/2 x are x=-(-5+sqrt(89))/4 ,x=(5+sqrt(89))/4

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

x = - \frac{- 5 + 89}{4}, x = \frac{5 + 89}{4}

Decimal Notation

x = - 1.10849 \dots, x = 3.60849 \dots

Solution steps

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

Multiply both sides by

2

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

Move

x

to the left side

- 2 x^{2} + 5 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 5 \pm 5 ^{2} - 4 ( - 2 ) \cdot 8}{2 ( - 2 )}

5^{2} - 4 (- 2) \cdot 8 = 89

x_{1, 2} = \frac{- 5 \pm 89}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 5 + 89}{2 ( - 2 )}, x_{2} = \frac{- 5 - 89}{2 ( - 2 )}

x = \frac{- 5 + 89}{2 ( - 2 )} : - \frac{- 5 + 89}{4}

x = \frac{- 5 - 89}{2 ( - 2 )} : \frac{5 + 89}{4}

The solutions to the quadratic equation are:

x = - \frac{- 5 + 89}{4}, x = \frac{5 + 89}{4}

x^{2} - x - 20 = 0

A = π x^{2}

1.5 x^{2} - 5 x - 2.5 = 0

4 t^{2} - 196 = 0

4 x (x - 1) - 3 x = 2 x

What are the solutions to the equation 4+2x-x^2=-1/2 x ?
The solutions to the equation 4+2x-x^2=-1/2 x are x=-(-5+sqrt(89))/4 ,x=(5+sqrt(89))/4
Find the zeros of 4+2x-x^2=-1/2 x
The zeros of 4+2x-x^2=-1/2 x are x=-(-5+sqrt(89))/4 ,x=(5+sqrt(89))/4