Solve 2c^2h^4 = c^4h^6 h^2

Question

Solve the equation

Solve for c

Solve for h

c = 0 c = \frac{2}{h ^{2}} c = - \frac{2}{h ^{2}}

Evaluate

2 c^{2} h^{4} = c^{4} h^{6} \times h^{2}

Multiply

More Steps

Evaluate

c^{4} h^{6} \times h^{2}

Multiply the terms with the same base by adding their exponents

c^{4} h^{6 + 2}

Add the numbers

c^{4} h^{8}

2 c^{2} h^{4} = c^{4} h^{8}

Rewrite the expression

2 h^{4} c^{2} = h^{8} c^{4}

Add or subtract both sides

2 h^{4} c^{2} - h^{8} c^{4} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solution

More Steps

Evaluate

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

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

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

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

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

Divide both sides

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

Divide the numbers

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{2}{h ^{4}}

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

\frac{2}{h ^{4}}

Simplify the radical expression

\frac{2}{h ^{2}}

c = \pm \frac{2}{h ^{2}}

Separate the equation into 2 possible cases

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

c = 0 c = \frac{2}{h ^{2}} c = - \frac{2}{h ^{2}}

Show Solution