Solve 4c^27c - 5 = 0

Question

Solve the equation

c = \frac{3 490}{14}

Alternative Form

c \approx 0.563124

Evaluate

4 c^{2} \times 7 c - 5 = 0

Multiply

More Steps

Evaluate

4 c^{2} \times 7 c

Multiply the terms

28 c^{2} \times c

Multiply the terms with the same base by adding their exponents

28 c^{2 + 1}

Add the numbers

28 c^{3}

28 c^{3} - 5 = 0

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

28 c^{3} = 0 + 5

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

28 c^{3} = 5

Divide both sides

\frac{28 c ^{3}}{28} = \frac{5}{28}

Divide the numbers

c^{3} = \frac{5}{28}

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

3 c^{3} = 3 \frac{5}{28}

Calculate

c = 3 \frac{5}{28}

Solution

More Steps

Evaluate

3 \frac{5}{28}

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

\frac{3 5}{3 28}

Multiply by the Conjugate

\frac{3 5 \times 3 2 8 ^{2}}{3 28 \times 3 2 8 ^{2}}

Simplify

\frac{3 5 \times 2 3 98}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 2398

Multiply the terms

3490 \times 2

Use the commutative property to reorder the terms

23490

\frac{2 3 490}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

328 \times 3 2 8^{2}

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

3 28 \times 2 8^{2}

Calculate the product

3 2 8^{3}

Reduce the index of the radical and exponent with 3

28

\frac{2 3 490}{28}

Cancel out the common factor 2

\frac{3 490}{14}

c = \frac{3 490}{14}

Alternative Form

c \approx 0.563124

Show Solution