Solve c^2h^2+h^2=c^2h^6

Question

Solve the equation

$Solve for h$

h = 0 h = \frac{4 c ^{4} + c ^{2}}{∣ c ∣} h = - \frac{4 c ^{4} + c ^{2}}{∣ c ∣}

Evaluate

c^{2} h^{2} + h^{2} = c^{2} h^{6}

Collect like terms by calculating the sum or difference of their coefficients

(c^{2} + 1) h^{2} = c^{2} h^{6}

Add or subtract both sides

(c^{2} + 1) h^{2} - c^{2} h^{6} = 0

Factor the expression

h^{2} (c^{2} + 1 - c^{2} h^{4}) = 0

Separate the equation into 2 possible cases

h^{2} = 0 c^{2} + 1 - c^{2} h^{4} = 0

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

h = 0 c^{2} + 1 - c^{2} h^{4} = 0

Solution

More Steps

Evaluate

c^{2} + 1 - c^{2} h^{4} = 0

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

- c^{2} h^{4} = 0 - (c^{2} + 1)

Subtract the terms

More Steps

Evaluate

0 - (c^{2} + 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

0 - c^{2} - 1

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

- c^{2} - 1

- c^{2} h^{4} = - c^{2} - 1

Divide both sides

\frac{- c ^{2} h ^{4}}{- c ^{2}} = \frac{- c ^{2} - 1}{- c ^{2}}

Divide the numbers

h^{4} = \frac{- c ^{2} - 1}{- c ^{2}}

Divide the numbers

h^{4} = \frac{c ^{2} + 1}{c ^{2}}

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

h = \pm 4 \frac{c ^{2} + 1}{c ^{2}}

Simplify the expression

More Steps

Evaluate

4 \frac{c ^{2} + 1}{c ^{2}}

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

\frac{4 c ^{2} + 1}{4 c ^{2}}

Simplify the radical expression

\frac{4 c ^{2} + 1}{∣ c ∣}

Multiply by the Conjugate

\frac{4 c ^{2} + 1 \times ∣ c ∣}{∣ c ∣ \times ∣ c ∣}

Calculate

\frac{4 c ^{2} + 1 \times ∣ c ∣}{∣ c ∣}

Calculate

\frac{4 c ^{4} + c ^{2}}{∣ c ∣}

h = \pm \frac{4 c ^{4} + c ^{2}}{∣ c ∣}

Separate the equation into 2 possible cases

h = \frac{4 c ^{4} + c ^{2}}{∣ c ∣} h = - \frac{4 c ^{4} + c ^{2}}{∣ c ∣}

h = 0 h = \frac{4 c ^{4} + c ^{2}}{∣ c ∣} h = - \frac{4 c ^{4} + c ^{2}}{∣ c ∣}

Show Solution

C^2h^2+h^2=c^2h^6

Solve the equation

Solve for h

$Solve for h$