Solve \((x-h)^{2} k^{2}=r^{2}\)

Evaluate

(x - h)^{2} k^{2} = r^{2}

Use the commutative property to reorder the terms

k^{2} (x - h)^{2} = r^{2}

Divide both sides

\frac{k ^{2} ( x - h ) ^{2}}{k ^{2}} = \frac{r ^{2}}{k ^{2}}

Divide the numbers

(x - h)^{2} = \frac{r ^{2}}{k ^{2}}

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

x - h = \pm \frac{r ^{2}}{k ^{2}}

Simplify the expression

More Steps

x - h = \pm \frac{∣ r ∣}{∣ k ∣}

Remove the absolute value bars

x - h = \pm \frac{r}{∣ k ∣}

Separate the equation into 2 possible cases

x - h = \frac{r}{∣ k ∣} x - h = - \frac{r}{∣ k ∣}

Calculate

More Steps

x = \frac{r + h ∣ k ∣}{∣ k ∣} x - h = - \frac{r}{∣ k ∣}

Solution

More Steps

x = \frac{r + h ∣ k ∣}{∣ k ∣} x = \frac{- r + h ∣ k ∣}{∣ k ∣}

Solve the equation