Solve c^4h8o^2 c=c

Question

Solve the equation

Solve for c

Solve for h

Solve for o

c = 0 c = \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣} c = - \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣}

Evaluate

c^{4} h \times 8 o^{2} c = c

Multiply

More Steps

Evaluate

c^{4} h \times 8 o^{2} c

Multiply the terms with the same base by adding their exponents

c^{4 + 1} h \times 8 o^{2}

Add the numbers

c^{5} h \times 8 o^{2}

Use the commutative property to reorder the terms

8 c^{5} h o^{2}

8 c^{5} h o^{2} = c

Rewrite the expression

8 h o^{2} c^{5} = c

Add or subtract both sides

8 h o^{2} c^{5} - c = 0

Factor the expression

c (8 h o^{2} c^{4} - 1) = 0

Separate the equation into 2 possible cases

c = 0 8 h o^{2} c^{4} - 1 = 0

Solution

More Steps

Evaluate

8 h o^{2} c^{4} - 1 = 0

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

8 h o^{2} c^{4} = 0 + 1

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

8 h o^{2} c^{4} = 1

Divide both sides

\frac{8 h o ^{2} c ^{4}}{8 h o ^{2}} = \frac{1}{8 h o ^{2}}

Divide the numbers

c^{4} = \frac{1}{8 h o ^{2}}

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

c = \pm 4 \frac{1}{8 h o ^{2}}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8 h o ^{2}}

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

\frac{4 1}{4 8 h o ^{2}}

Simplify the radical expression

\frac{1}{4 8 h o ^{2}}

Multiply by the Conjugate

\frac{1 \times 4 8 ^{3} h ^{3} o ^{2}}{4 8 h o ^{2} \times 4 8 ^{3} h ^{3} o ^{2}}

Calculate

\frac{1 \times 4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Calculate

\frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

c = \pm \frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Separate the equation into 2 possible cases

c = \frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣} c = - \frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Calculate

More Steps

Evaluate

\frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Rewrite the expression

\frac{2 ^{2} 4 2 o ^{2} h ^{3}}{8 ∣ h o ∣}

Reduce the fraction

\frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣}

c = \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣} c = - \frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Calculate

More Steps

Evaluate

- \frac{4 8 ^{3} h ^{3} o ^{2}}{8 ∣ h o ∣}

Rewrite the expression

- \frac{2 ^{2} 4 2 o ^{2} h ^{3}}{8 ∣ h o ∣}

Reduce the fraction

- \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣}

c = \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣} c = - \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣}

c = 0 c = \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣} c = - \frac{4 2 o ^{2} h ^{3}}{2 ∣ h o ∣}

Show Solution