Solve dd^3023-100

Question

Simplify the expression

23 d^{4} - 100

Evaluate

d \times d^{3} \times 23 - 100

Solution

More Steps

Evaluate

d \times d^{3} \times 23

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 23

Add the numbers

d^{4} \times 23

Use the commutative property to reorder the terms

23 d^{4}

23 d^{4} - 100

Show Solution

d_{1} = - \frac{4 1216700}{23}, d_{2} = \frac{4 1216700}{23}

Alternative Form

d_{1} \approx - 1.444003, d_{2} \approx 1.444003

Evaluate

d \times d^{3} \times 23 - 100

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

d \times d^{3} \times 23 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 23

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 23

Add the numbers

d^{4} \times 23

Use the commutative property to reorder the terms

23 d^{4}

23 d^{4} - 100 = 0

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

23 d^{4} = 0 + 100

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

23 d^{4} = 100

Divide both sides

\frac{23 d ^{4}}{23} = \frac{100}{23}

Divide the numbers

d^{4} = \frac{100}{23}

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

d = \pm 4 \frac{100}{23}

Simplify the expression

More Steps

Evaluate

4 \frac{100}{23}

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

\frac{4 100}{4 23}

Simplify the radical expression

\frac{10}{4 23}

Multiply by the Conjugate

\frac{10 \times 4 2 3 ^{3}}{4 23 \times 4 2 3 ^{3}}

Simplify

\frac{10 \times 4 12167}{4 23 \times 4 2 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

10 \times 412167

Use n a = mn a^{m} to expand the expression

4 1 0^{2} \times 412167

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

4 1 0^{2} \times 12167

Calculate the product

41216700

\frac{4 1216700}{4 23 \times 4 2 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

423 \times 4 2 3^{3}

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

4 23 \times 2 3^{3}

Calculate the product

4 2 3^{4}

Reduce the index of the radical and exponent with 4

23

\frac{4 1216700}{23}

d = \pm \frac{4 1216700}{23}

Separate the equation into 2 possible cases

d = \frac{4 1216700}{23} d = - \frac{4 1216700}{23}

Solution

d_{1} = - \frac{4 1216700}{23}, d_{2} = \frac{4 1216700}{23}

Alternative Form

d_{1} \approx - 1.444003, d_{2} \approx 1.444003

Show Solution