Solve 1/5 {[4/9*(1/2x^2/4-1/9)]}

Question

Simplify the expression

\frac{9 x ^{2} - 8}{810}

Show Solution

x_{1} = - \frac{2 2}{3}, x_{2} = \frac{2 2}{3}

Alternative Form

x_{1} \approx - 0.942809, x_{2} \approx 0.942809

Evaluate

\frac{1}{5} (\frac{4}{9} (\frac{1}{2} \times \frac{x ^{2}}{4} - \frac{1}{9}))

To find the roots of the expression,set the expression equal to 0

\frac{1}{5} (\frac{4}{9} (\frac{1}{2} \times \frac{x ^{2}}{4} - \frac{1}{9})) = 0

Multiply the terms

More Steps

\frac{1}{5} (\frac{4}{9} (\frac{x ^{2}}{8} - \frac{1}{9})) = 0

Subtract the terms

More Steps

\frac{1}{5} (\frac{4}{9} \times \frac{9 x ^{2} - 8}{72}) = 0

Multiply the terms

More Steps

\frac{1}{5} \times \frac{9 x ^{2} - 8}{162} = 0

Multiply the terms

More Steps

\frac{9 x ^{2} - 8}{810} = 0

Simplify

9 x^{2} - 8 = 0

Move the constant to the right side

9 x^{2} = 8

Divide both sides

\frac{9 x ^{2}}{9} = \frac{8}{9}

Divide the numbers

x^{2} = \frac{8}{9}

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

x = \pm \frac{8}{9}

Simplify the expression

More Steps

x = \pm \frac{2 2}{3}

Separate the equation into 2 possible cases

x = \frac{2 2}{3} x = - \frac{2 2}{3}

Solution

x_{1} = - \frac{2 2}{3}, x_{2} = \frac{2 2}{3}

Alternative Form

x_{1} \approx - 0.942809, x_{2} \approx 0.942809

Show Solution