Solve dd^5227-234

Question

Simplify the expression

227 d^{6} - 234

Evaluate

d \times d^{5} \times 227 - 234

Solution

More Steps

Evaluate

d \times d^{5} \times 227

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 227

Add the numbers

d^{6} \times 227

Use the commutative property to reorder the terms

227 d^{6}

227 d^{6} - 234

Show Solution

d_{1} = - \frac{6 234 \times 22 7 ^{5}}{227}, d_{2} = \frac{6 234 \times 22 7 ^{5}}{227}

Alternative Form

d_{1} \approx - 1.005075, d_{2} \approx 1.005075

Evaluate

d \times d^{5} \times 227 - 234

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

d \times d^{5} \times 227 - 234 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 227

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 227

Add the numbers

d^{6} \times 227

Use the commutative property to reorder the terms

227 d^{6}

227 d^{6} - 234 = 0

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

227 d^{6} = 0 + 234

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

227 d^{6} = 234

Divide both sides

\frac{227 d ^{6}}{227} = \frac{234}{227}

Divide the numbers

d^{6} = \frac{234}{227}

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

d = \pm 6 \frac{234}{227}

Simplify the expression

More Steps

Evaluate

6 \frac{234}{227}

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

\frac{6 234}{6 227}

Multiply by the Conjugate

\frac{6 234 \times 6 22 7 ^{5}}{6 227 \times 6 22 7 ^{5}}

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

\frac{6 234 \times 22 7 ^{5}}{6 227 \times 6 22 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

6227 \times 6 22 7^{5}

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

6 227 \times 22 7^{5}

Calculate the product

6 22 7^{6}

Reduce the index of the radical and exponent with 6

227

\frac{6 234 \times 22 7 ^{5}}{227}

d = \pm \frac{6 234 \times 22 7 ^{5}}{227}

Separate the equation into 2 possible cases

d = \frac{6 234 \times 22 7 ^{5}}{227} d = - \frac{6 234 \times 22 7 ^{5}}{227}

Solution

d_{1} = - \frac{6 234 \times 22 7 ^{5}}{227}, d_{2} = \frac{6 234 \times 22 7 ^{5}}{227}

Alternative Form

d_{1} \approx - 1.005075, d_{2} \approx 1.005075

Show Solution