Solve 8dd^355129-171

Question

Simplify the expression

441032 d^{4} - 171

Evaluate

8 d \times d^{3} \times 55129 - 171

Solution

More Steps

Evaluate

8 d \times d^{3} \times 55129

Multiply the terms

441032 d \times d^{3}

Multiply the terms with the same base by adding their exponents

441032 d^{1 + 3}

Add the numbers

441032 d^{4}

441032 d^{4} - 171

Show Solution

d_{1} = - \frac{4 171 \times 44103 2 ^{3}}{441032}, d_{2} = \frac{4 171 \times 44103 2 ^{3}}{441032}

Alternative Form

d_{1} \approx - 0.140324, d_{2} \approx 0.140324

Evaluate

8 d \times d^{3} \times 55129 - 171

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

8 d \times d^{3} \times 55129 - 171 = 0

Multiply

More Steps

Multiply the terms

8 d \times d^{3} \times 55129

Multiply the terms

441032 d \times d^{3}

Multiply the terms with the same base by adding their exponents

441032 d^{1 + 3}

Add the numbers

441032 d^{4}

441032 d^{4} - 171 = 0

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

441032 d^{4} = 0 + 171

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

441032 d^{4} = 171

Divide both sides

\frac{441032 d ^{4}}{441032} = \frac{171}{441032}

Divide the numbers

d^{4} = \frac{171}{441032}

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

d = \pm 4 \frac{171}{441032}

Simplify the expression

More Steps

Evaluate

4 \frac{171}{441032}

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

\frac{4 171}{4 441032}

Multiply by the Conjugate

\frac{4 171 \times 4 44103 2 ^{3}}{4 441032 \times 4 44103 2 ^{3}}

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

\frac{4 171 \times 44103 2 ^{3}}{4 441032 \times 4 44103 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

4441032 \times 4 44103 2^{3}

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

4 441032 \times 44103 2^{3}

Calculate the product

4 44103 2^{4}

Reduce the index of the radical and exponent with 4

441032

\frac{4 171 \times 44103 2 ^{3}}{441032}

d = \pm \frac{4 171 \times 44103 2 ^{3}}{441032}

Separate the equation into 2 possible cases

d = \frac{4 171 \times 44103 2 ^{3}}{441032} d = - \frac{4 171 \times 44103 2 ^{3}}{441032}

Solution

d_{1} = - \frac{4 171 \times 44103 2 ^{3}}{441032}, d_{2} = \frac{4 171 \times 44103 2 ^{3}}{441032}

Alternative Form

d_{1} \approx - 0.140324, d_{2} \approx 0.140324

Show Solution