What are the solutions to the equation 8+4z-z^2=0 ?

The solutions to the equation 8+4z-z^2=0 are z=-2(sqrt(3)-1),z=2(1+sqrt(3))

Find the zeros of 8+4z-z^2=0

The zeros of 8+4z-z^2=0 are z=-2(sqrt(3)-1),z=2(1+sqrt(3))

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8 + 4 z - z^{2} = 0

z = - 2 (3 - 1), z = 2 (1 + 3)

Decimal Notation

z = - 1.46410 \dots, z = 5.46410 \dots

Solution steps

8 + 4 z - z^{2} = 0

Write in the standard form

a x^{2} + b x + c = 0

- z^{2} + 4 z + 8 = 0

Solve with the quadratic formula

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

4^{2} - 4 (- 1) \cdot 8 = 43

z_{1, 2} = \frac{- 4 \pm 4 3}{2 ( - 1 )}

Separate the solutions

z_{1} = \frac{- 4 + 4 3}{2 ( - 1 )}, z_{2} = \frac{- 4 - 4 3}{2 ( - 1 )}

z = \frac{- 4 + 4 3}{2 ( - 1 )} : - 2 (3 - 1)

z = \frac{- 4 - 4 3}{2 ( - 1 )} : 2 (1 + 3)

The solutions to the quadratic equation are:

z = - 2 (3 - 1), z = 2 (1 + 3)

2 x^{2} - 7 = 7 (x - 1) + 2 x

5 x + 3 = 4 x^{2}

x, 36 x^{2} + 16 y^{2} - 9 z^{2} - 144 = 0

3 x^{2} - 160 x + 1600 = 0

\frac{309}{16} xx + \frac{43}{12} = \frac{73}{12}

What are the solutions to the equation 8+4z-z^2=0 ?
The solutions to the equation 8+4z-z^2=0 are z=-2(sqrt(3)-1),z=2(1+sqrt(3))
Find the zeros of 8+4z-z^2=0
The zeros of 8+4z-z^2=0 are z=-2(sqrt(3)-1),z=2(1+sqrt(3))