Solve 5k^(2 ) 13k-46=0

Question

Solve the equation

k = \frac{3 194350}{65}

Alternative Form

k \approx 0.891145

Evaluate

5 k^{2} \times 13 k - 46 = 0

Multiply

More Steps

Evaluate

5 k^{2} \times 13 k

Multiply the terms

65 k^{2} \times k

Multiply the terms with the same base by adding their exponents

65 k^{2 + 1}

Add the numbers

65 k^{3}

65 k^{3} - 46 = 0

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

65 k^{3} = 0 + 46

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

65 k^{3} = 46

Divide both sides

\frac{65 k ^{3}}{65} = \frac{46}{65}

Divide the numbers

k^{3} = \frac{46}{65}

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

3 k^{3} = 3 \frac{46}{65}

Calculate

k = 3 \frac{46}{65}

Solution

More Steps

Evaluate

3 \frac{46}{65}

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

\frac{3 46}{3 65}

Multiply by the Conjugate

\frac{3 46 \times 3 6 5 ^{2}}{3 65 \times 3 6 5 ^{2}}

Simplify

\frac{3 46 \times 3 4225}{3 65 \times 3 6 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

346 \times 34225

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

3 46 \times 4225

Calculate the product

3194350

\frac{3 194350}{3 65 \times 3 6 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

365 \times 3 6 5^{2}

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

3 65 \times 6 5^{2}

Calculate the product

3 6 5^{3}

Reduce the index of the radical and exponent with 3

65

\frac{3 194350}{65}

k = \frac{3 194350}{65}

Alternative Form

k \approx 0.891145

Show Solution