Solve 3c^2 27c-108=0

Question

Solve the equation

c = \frac{3 36}{3}

Alternative Form

c \approx 1.100642

Evaluate

3 c^{2} \times 27 c - 108 = 0

Multiply

More Steps

Evaluate

3 c^{2} \times 27 c

Multiply the terms

81 c^{2} \times c

Multiply the terms with the same base by adding their exponents

81 c^{2 + 1}

Add the numbers

81 c^{3}

81 c^{3} - 108 = 0

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

81 c^{3} = 0 + 108

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

81 c^{3} = 108

Divide both sides

\frac{81 c ^{3}}{81} = \frac{108}{81}

Divide the numbers

c^{3} = \frac{108}{81}

Cancel out the common factor 27

c^{3} = \frac{4}{3}

Take the 3 -th root on both sides of the equation

3 c^{3} = 3 \frac{4}{3}

Calculate

c = 3 \frac{4}{3}

Solution

More Steps

Evaluate

3 \frac{4}{3}

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

\frac{3 4}{3 3}

Multiply by the Conjugate

\frac{3 4 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 4 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 39

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

3 4 \times 9

Calculate the product

336

\frac{3 36}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 36}{3}

c = \frac{3 36}{3}

Alternative Form

c \approx 1.100642

Show Solution