Solve k^410-494(3)

Question

Simplify the expression

10 k^{4} - 1482

Evaluate

k^{4} \times 10 - 494 \times 3

Use the commutative property to reorder the terms

10 k^{4} - 494 \times 3

Solution

10 k^{4} - 1482

Show Solution

2 (5 k^{4} - 741)

Evaluate

k^{4} \times 10 - 494 \times 3

Use the commutative property to reorder the terms

10 k^{4} - 494 \times 3

Multiply the numbers

10 k^{4} - 1482

Solution

2 (5 k^{4} - 741)

Show Solution

k_{1} = - \frac{4 92625}{5}, k_{2} = \frac{4 92625}{5}

Alternative Form

k_{1} \approx - 3.489089, k_{2} \approx 3.489089

Evaluate

k^{4} \times 10 - 494 \times 3

To find the roots of the expression,set the expression equal to 0

k^{4} \times 10 - 494 \times 3 = 0

Use the commutative property to reorder the terms

10 k^{4} - 494 \times 3 = 0

Multiply the numbers

10 k^{4} - 1482 = 0

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

10 k^{4} = 0 + 1482

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

10 k^{4} = 1482

Divide both sides

\frac{10 k ^{4}}{10} = \frac{1482}{10}

Divide the numbers

k^{4} = \frac{1482}{10}

Cancel out the common factor 2

k^{4} = \frac{741}{5}

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

k = \pm 4 \frac{741}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{741}{5}

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

\frac{4 741}{4 5}

Multiply by the Conjugate

\frac{4 741 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 741 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

4741 \times 4125

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

4 741 \times 125

Calculate the product

492625

\frac{4 92625}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 92625}{5}

k = \pm \frac{4 92625}{5}

Separate the equation into 2 possible cases

k = \frac{4 92625}{5} k = - \frac{4 92625}{5}

Solution

k_{1} = - \frac{4 92625}{5}, k_{2} = \frac{4 92625}{5}

Alternative Form

k_{1} \approx - 3.489089, k_{2} \approx 3.489089

Show Solution