What are the solutions to the equation x=-x^2+2x+3 ?

The solutions to the equation x=-x^2+2x+3 are x=-(-1+sqrt(13))/2 ,x=(1+sqrt(13))/2

Find the zeros of x=-x^2+2x+3

The zeros of x=-x^2+2x+3 are x=-(-1+sqrt(13))/2 ,x=(1+sqrt(13))/2

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

x = - \frac{- 1 + 13}{2}, x = \frac{1 + 13}{2}

Solution steps

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

Switch sides

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

Move

x

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 ) \cdot 3}{2 ( - 1 )}

1^{2} - 4 (- 1) \cdot 3 = 13

x_{1, 2} = \frac{- 1 \pm 13}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 1 + 13}{2 ( - 1 )}, x_{2} = \frac{- 1 - 13}{2 ( - 1 )}

x = \frac{- 1 + 13}{2 ( - 1 )} : - \frac{- 1 + 13}{2}

x = \frac{- 1 - 13}{2 ( - 1 )} : \frac{1 + 13}{2}

The solutions to the quadratic equation are:

x = - \frac{- 1 + 13}{2}, x = \frac{1 + 13}{2}

12 x^{2} + 18 x + 6 = 0

(8 x - 10) (x - 1) = 0

x^{2} + 56 x = 8.16

x, 2 x^{2} + 7 x + 5 = 0

x (4 x - 1) = 5

What are the solutions to the equation x=-x^2+2x+3 ?
The solutions to the equation x=-x^2+2x+3 are x=-(-1+sqrt(13))/2 ,x=(1+sqrt(13))/2
Find the zeros of x=-x^2+2x+3
The zeros of x=-x^2+2x+3 are x=-(-1+sqrt(13))/2 ,x=(1+sqrt(13))/2