Solve -13c 12c^3c-4=-18

Question

Solve the equation

c = \frac{5 7 \times 7 8 ^{4}}{78}

Alternative Form

c \approx 0.617448

Evaluate

- 13 c \times 12 c^{3} \times c - 4 = - 18

Multiply

More Steps

Evaluate

- 13 c \times 12 c^{3} \times c

Multiply the terms

- 156 c \times c^{3} \times c

Multiply the terms with the same base by adding their exponents

- 156 c^{1 + 3 + 1}

Add the numbers

- 156 c^{5}

- 156 c^{5} - 4 = - 18

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

- 156 c^{5} = - 18 + 4

Add the numbers

- 156 c^{5} = - 14

Change the signs on both sides of the equation

156 c^{5} = 14

Divide both sides

\frac{156 c ^{5}}{156} = \frac{14}{156}

Divide the numbers

c^{5} = \frac{14}{156}

Cancel out the common factor 2

c^{5} = \frac{7}{78}

Take the 5 -th root on both sides of the equation

5 c^{5} = 5 \frac{7}{78}

Calculate

c = 5 \frac{7}{78}

Solution

More Steps

Evaluate

5 \frac{7}{78}

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

\frac{5 7}{5 78}

Multiply by the Conjugate

\frac{5 7 \times 5 7 8 ^{4}}{5 78 \times 5 7 8 ^{4}}

The product of roots with the same index is equal to the root of the product

\frac{5 7 \times 7 8 ^{4}}{5 78 \times 5 7 8 ^{4}}

Multiply the numbers

More Steps

Evaluate

578 \times 5 7 8^{4}

The product of roots with the same index is equal to the root of the product

5 78 \times 7 8^{4}

Calculate the product

5 7 8^{5}

Reduce the index of the radical and exponent with 5

78

\frac{5 7 \times 7 8 ^{4}}{78}

c = \frac{5 7 \times 7 8 ^{4}}{78}

Alternative Form

c \approx 0.617448

Show Solution