Solve v^2=n^2(a^2-x^2)

Evaluate

v^{2} = n^{2} (a^{2} - x^{2})

Swap the sides of the equation

n^{2} (a^{2} - x^{2}) = v^{2}

Divide both sides

\frac{n ^{2} ( a ^{2} - x ^{2} )}{n ^{2}} = \frac{v ^{2}}{n ^{2}}

Divide the numbers

a^{2} - x^{2} = \frac{v ^{2}}{n ^{2}}

Move the constant to the right side

- x^{2} = \frac{v ^{2}}{n ^{2}} - a^{2}

Subtract the terms

More Steps

- x^{2} = \frac{v ^{2} - n ^{2} a ^{2}}{n ^{2}}

Change the signs on both sides of the equation

x^{2} = \frac{- v ^{2} + n ^{2} a ^{2}}{n ^{2}}

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

x = \pm \frac{- v ^{2} + n ^{2} a ^{2}}{n ^{2}}

Simplify the expression

More Steps

x = \pm \frac{- v ^{2} + n ^{2} a ^{2}}{∣ n ∣}

Separate the equation into 2 possible cases

x = \frac{- v ^{2} + n ^{2} a ^{2}}{∣ n ∣} x = - \frac{- v ^{2} + n ^{2} a ^{2}}{∣ n ∣}

Simplify

x = \frac{- v ^{2} + a ^{2} n ^{2}}{∣ n ∣} x = - \frac{- v ^{2} + n ^{2} a ^{2}}{∣ n ∣}

Solution

x = \frac{- v ^{2} + a ^{2} n ^{2}}{∣ n ∣} x = - \frac{- v ^{2} + a ^{2} n ^{2}}{∣ n ∣}

Solve the equation