Solve 1-(1-p)^2=8/9

Evaluate

1 - (1 - p)^{2} = \frac{8}{9}

Add or subtract both sides

- (1 - p)^{2} = - \frac{1}{9}

Divide both sides

\frac{- ( 1 - p ) ^{2}}{- 1} = \frac{- \frac{1}{9}}{- 1}

Divide the numbers

(1 - p)^{2} = \frac{1}{9}

Take the root of both sides of the equation and remember to use both positive and negative roots

1 - p = \pm \frac{1}{9}

Simplify the expression

1 - p = \pm \frac{1}{3}

Separate the equation into 2 possible cases

1 - p = \frac{1}{3} 1 - p = - \frac{1}{3}

Solve the equation

More Steps

p = \frac{2}{3} 1 - p = - \frac{1}{3}

Solve the equation

More Steps

p = \frac{2}{3} p = \frac{4}{3}

Solution

p_{1} = \frac{2}{3}, p_{2} = \frac{4}{3}

Alternative Form

p_{1} = 0. \dot{6}, p_{2} = 1. \dot{3}

1 (1 P)^2=8/9