Solve dd^5708-410

Question

Simplify the expression

708 d^{6} - 410

Evaluate

d \times d^{5} \times 708 - 410

Solution

More Steps

Evaluate

d \times d^{5} \times 708

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 708

Add the numbers

d^{6} \times 708

Use the commutative property to reorder the terms

708 d^{6}

708 d^{6} - 410

Show Solution

Factor the expression

2 (354 d^{6} - 205)

Evaluate

d \times d^{5} \times 708 - 410

Multiply

More Steps

Evaluate

d \times d^{5} \times 708

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 708

Add the numbers

d^{6} \times 708

Use the commutative property to reorder the terms

708 d^{6}

708 d^{6} - 410

Solution

2 (354 d^{6} - 205)

Show Solution

Find the roots

d_{1} = - \frac{6 205 \times 35 4 ^{5}}{354}, d_{2} = \frac{6 205 \times 35 4 ^{5}}{354}

Alternative Form

d_{1} \approx - 0.912974, d_{2} \approx 0.912974

Evaluate

d \times d^{5} \times 708 - 410

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

d \times d^{5} \times 708 - 410 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 708

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 708

Add the numbers

d^{6} \times 708

Use the commutative property to reorder the terms

708 d^{6}

708 d^{6} - 410 = 0

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

708 d^{6} = 0 + 410

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

708 d^{6} = 410

Divide both sides

\frac{708 d ^{6}}{708} = \frac{410}{708}

Divide the numbers

d^{6} = \frac{410}{708}

Cancel out the common factor 2

d^{6} = \frac{205}{354}

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

d = \pm 6 \frac{205}{354}

Simplify the expression

More Steps

Evaluate

6 \frac{205}{354}

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

\frac{6 205}{6 354}

Multiply by the Conjugate

\frac{6 205 \times 6 35 4 ^{5}}{6 354 \times 6 35 4 ^{5}}

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

\frac{6 205 \times 35 4 ^{5}}{6 354 \times 6 35 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

6354 \times 6 35 4^{5}

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

6 354 \times 35 4^{5}

Calculate the product

6 35 4^{6}

Reduce the index of the radical and exponent with 6

354

\frac{6 205 \times 35 4 ^{5}}{354}

d = \pm \frac{6 205 \times 35 4 ^{5}}{354}

Separate the equation into 2 possible cases

d = \frac{6 205 \times 35 4 ^{5}}{354} d = - \frac{6 205 \times 35 4 ^{5}}{354}

Solution

d_{1} = - \frac{6 205 \times 35 4 ^{5}}{354}, d_{2} = \frac{6 205 \times 35 4 ^{5}}{354}

Alternative Form

d_{1} \approx - 0.912974, d_{2} \approx 0.912974

Show Solution