Solve h^2=h1 (h^2s h1/n)

Question

Solve the equation

Solve for h

Solve for n

Solve for s

h = 0 h = \frac{n s}{∣ s ∣} h = - \frac{n s}{∣ s ∣}

Evaluate

h^{2} = h \times 1 \times (h^{2} s h \times \frac{1}{n})

Remove the parentheses

h^{2} = h \times 1 \times h^{2} s h \times \frac{1}{n}

Multiply the terms

More Steps

Evaluate

h \times 1 \times h^{2} s h \times \frac{1}{n}

Rewrite the expression

h \times h^{2} s h \times \frac{1}{n}

Multiply the terms with the same base by adding their exponents

h^{1 + 2 + 1} s \times \frac{1}{n}

Add the numbers

h^{4} s \times \frac{1}{n}

Multiply the terms

\frac{h ^{4} s}{n}

h^{2} = \frac{h ^{4} s}{n}

Rewrite the expression

h^{2} = \frac{s h ^{4}}{n}

Cross multiply

h^{2} n = s h^{4}

Simplify the equation

n h^{2} = s h^{4}

Add or subtract both sides

n h^{2} - s h^{4} = 0

Factor the expression

h^{2} (n - s h^{2}) = 0

Separate the equation into 2 possible cases

h^{2} = 0 n - s h^{2} = 0

The only way a power can be 0 is when the base equals 0

h = 0 n - s h^{2} = 0

Solution

More Steps

Evaluate

n - s h^{2} = 0

Move the expression to the right-hand side and change its sign

- s h^{2} = 0 - n

Removing 0 doesn't change the value,so remove it from the expression

- s h^{2} = - n

Divide both sides

\frac{- s h ^{2}}{- s} = \frac{- n}{- s}

Divide the numbers

h^{2} = \frac{- n}{- s}

Divide the numbers

h^{2} = \frac{n}{s}

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

h = \pm \frac{n}{s}

Simplify the expression

More Steps

Evaluate

\frac{n}{s}

Rewrite the expression

\frac{n s}{s \times s}

Calculate

\frac{n s}{s ^{2}}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{n s}{s ^{2}}

Simplify the radical expression

\frac{n s}{∣ s ∣}

h = \pm \frac{n s}{∣ s ∣}

Separate the equation into 2 possible cases

h = \frac{n s}{∣ s ∣} h = - \frac{n s}{∣ s ∣}

h = 0 h = \frac{n s}{∣ s ∣} h = - \frac{n s}{∣ s ∣}

Show Solution