Solve dd^5480-602

Question

Simplify the expression

480 d^{6} - 602

Evaluate

d \times d^{5} \times 480 - 602

Solution

More Steps

Evaluate

d \times d^{5} \times 480

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 480

Add the numbers

d^{6} \times 480

Use the commutative property to reorder the terms

480 d^{6}

480 d^{6} - 602

Show Solution

Factor the expression

2 (240 d^{6} - 301)

Evaluate

d \times d^{5} \times 480 - 602

Multiply

More Steps

Evaluate

d \times d^{5} \times 480

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 480

Add the numbers

d^{6} \times 480

Use the commutative property to reorder the terms

480 d^{6}

480 d^{6} - 602

Solution

2 (240 d^{6} - 301)

Show Solution

Find the roots

d_{1} = - \frac{6 301 \times 24 0 ^{5}}{240}, d_{2} = \frac{6 301 \times 24 0 ^{5}}{240}

Alternative Form

d_{1} \approx - 1.038467, d_{2} \approx 1.038467

Evaluate

d \times d^{5} \times 480 - 602

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

d \times d^{5} \times 480 - 602 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 480

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 480

Add the numbers

d^{6} \times 480

Use the commutative property to reorder the terms

480 d^{6}

480 d^{6} - 602 = 0

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

480 d^{6} = 0 + 602

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

480 d^{6} = 602

Divide both sides

\frac{480 d ^{6}}{480} = \frac{602}{480}

Divide the numbers

d^{6} = \frac{602}{480}

Cancel out the common factor 2

d^{6} = \frac{301}{240}

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

d = \pm 6 \frac{301}{240}

Simplify the expression

More Steps

Evaluate

6 \frac{301}{240}

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

\frac{6 301}{6 240}

Multiply by the Conjugate

\frac{6 301 \times 6 24 0 ^{5}}{6 240 \times 6 24 0 ^{5}}

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

\frac{6 301 \times 24 0 ^{5}}{6 240 \times 6 24 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

6240 \times 6 24 0^{5}

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

6 240 \times 24 0^{5}

Calculate the product

6 24 0^{6}

Reduce the index of the radical and exponent with 6

240

\frac{6 301 \times 24 0 ^{5}}{240}

d = \pm \frac{6 301 \times 24 0 ^{5}}{240}

Separate the equation into 2 possible cases

d = \frac{6 301 \times 24 0 ^{5}}{240} d = - \frac{6 301 \times 24 0 ^{5}}{240}

Solution

d_{1} = - \frac{6 301 \times 24 0 ^{5}}{240}, d_{2} = \frac{6 301 \times 24 0 ^{5}}{240}

Alternative Form

d_{1} \approx - 1.038467, d_{2} \approx 1.038467

Show Solution