What are the solutions to the equation z-z^2-1/8 =0 ?

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

Find the zeros of z-z^2-1/8 =0

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

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z - z^{2} - \frac{1}{8} = 0

z = \frac{2 - 2}{4}, z = \frac{2 + 2}{4}

Decimal Notation

z = 0.14644 \dots, z = 0.85355 \dots

Solution steps

z - z^{2} - \frac{1}{8} = 0

Multiply both sides by

8

- 8 z^{2} + 8 z - 1 = 0

Solve with the quadratic formula

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

8^{2} - 4 (- 8) (- 1) = 42

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

Separate the solutions

z_{1} = \frac{- 8 + 4 2}{2 ( - 8 )}, z_{2} = \frac{- 8 - 4 2}{2 ( - 8 )}

z = \frac{- 8 + 4 2}{2 ( - 8 )} : \frac{2 - 2}{4}

z = \frac{- 8 - 4 2}{2 ( - 8 )} : \frac{2 + 2}{4}

The solutions to the quadratic equation are:

z = \frac{2 - 2}{4}, z = \frac{2 + 2}{4}

x, x^{2} - 36 = 0

4 x^{2} - 64 x + 232 = 0

0 = 100 + 10 t - \frac{1.62}{2} t^{2}

x^{2} - 13 x + 5 = 0

q, 3 + q^{2} = \frac{G}{R}

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