Solve dd^5284-435

Question

Simplify the expression

284 d^{6} - 435

Evaluate

d \times d^{5} \times 284 - 435

Solution

More Steps

Evaluate

d \times d^{5} \times 284

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 284

Add the numbers

d^{6} \times 284

Use the commutative property to reorder the terms

284 d^{6}

284 d^{6} - 435

Show Solution

d_{1} = - \frac{6 435 \times 28 4 ^{5}}{284}, d_{2} = \frac{6 435 \times 28 4 ^{5}}{284}

Alternative Form

d_{1} \approx - 1.073648, d_{2} \approx 1.073648

Evaluate

d \times d^{5} \times 284 - 435

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

d \times d^{5} \times 284 - 435 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 284

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 284

Add the numbers

d^{6} \times 284

Use the commutative property to reorder the terms

284 d^{6}

284 d^{6} - 435 = 0

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

284 d^{6} = 0 + 435

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

284 d^{6} = 435

Divide both sides

\frac{284 d ^{6}}{284} = \frac{435}{284}

Divide the numbers

d^{6} = \frac{435}{284}

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

d = \pm 6 \frac{435}{284}

Simplify the expression

More Steps

Evaluate

6 \frac{435}{284}

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

\frac{6 435}{6 284}

Multiply by the Conjugate

\frac{6 435 \times 6 28 4 ^{5}}{6 284 \times 6 28 4 ^{5}}

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

\frac{6 435 \times 28 4 ^{5}}{6 284 \times 6 28 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

6284 \times 6 28 4^{5}

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

6 284 \times 28 4^{5}

Calculate the product

6 28 4^{6}

Reduce the index of the radical and exponent with 6

284

\frac{6 435 \times 28 4 ^{5}}{284}

d = \pm \frac{6 435 \times 28 4 ^{5}}{284}

Separate the equation into 2 possible cases

d = \frac{6 435 \times 28 4 ^{5}}{284} d = - \frac{6 435 \times 28 4 ^{5}}{284}

Solution

d_{1} = - \frac{6 435 \times 28 4 ^{5}}{284}, d_{2} = \frac{6 435 \times 28 4 ^{5}}{284}

Alternative Form

d_{1} \approx - 1.073648, d_{2} \approx 1.073648

Show Solution