Solve dd^5482-902

Question

Simplify the expression

482 d^{6} - 902

Evaluate

d \times d^{5} \times 482 - 902

Solution

More Steps

Evaluate

d \times d^{5} \times 482

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 482

Add the numbers

d^{6} \times 482

Use the commutative property to reorder the terms

482 d^{6}

482 d^{6} - 902

Show Solution

Factor the expression

2 (241 d^{6} - 451)

Evaluate

d \times d^{5} \times 482 - 902

Multiply

More Steps

Evaluate

d \times d^{5} \times 482

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 482

Add the numbers

d^{6} \times 482

Use the commutative property to reorder the terms

482 d^{6}

482 d^{6} - 902

Solution

2 (241 d^{6} - 451)

Show Solution

Find the roots

d_{1} = - \frac{6 451 \times 24 1 ^{5}}{241}, d_{2} = \frac{6 451 \times 24 1 ^{5}}{241}

Alternative Form

d_{1} \approx - 1.110094, d_{2} \approx 1.110094

Evaluate

d \times d^{5} \times 482 - 902

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

d \times d^{5} \times 482 - 902 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 482

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 482

Add the numbers

d^{6} \times 482

Use the commutative property to reorder the terms

482 d^{6}

482 d^{6} - 902 = 0

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

482 d^{6} = 0 + 902

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

482 d^{6} = 902

Divide both sides

\frac{482 d ^{6}}{482} = \frac{902}{482}

Divide the numbers

d^{6} = \frac{902}{482}

Cancel out the common factor 2

d^{6} = \frac{451}{241}

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

d = \pm 6 \frac{451}{241}

Simplify the expression

More Steps

Evaluate

6 \frac{451}{241}

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

\frac{6 451}{6 241}

Multiply by the Conjugate

\frac{6 451 \times 6 24 1 ^{5}}{6 241 \times 6 24 1 ^{5}}

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

\frac{6 451 \times 24 1 ^{5}}{6 241 \times 6 24 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

6241 \times 6 24 1^{5}

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

6 241 \times 24 1^{5}

Calculate the product

6 24 1^{6}

Reduce the index of the radical and exponent with 6

241

\frac{6 451 \times 24 1 ^{5}}{241}

d = \pm \frac{6 451 \times 24 1 ^{5}}{241}

Separate the equation into 2 possible cases

d = \frac{6 451 \times 24 1 ^{5}}{241} d = - \frac{6 451 \times 24 1 ^{5}}{241}

Solution

d_{1} = - \frac{6 451 \times 24 1 ^{5}}{241}, d_{2} = \frac{6 451 \times 24 1 ^{5}}{241}

Alternative Form

d_{1} \approx - 1.110094, d_{2} \approx 1.110094

Show Solution