Solve dd^3235-100

Question

Simplify the expression

235 d^{4} - 100

Evaluate

d \times d^{3} \times 235 - 100

Solution

More Steps

Evaluate

d \times d^{3} \times 235

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 235

Add the numbers

d^{4} \times 235

Use the commutative property to reorder the terms

235 d^{4}

235 d^{4} - 100

Show Solution

Factor the expression

5 (47 d^{4} - 20)

Evaluate

d \times d^{3} \times 235 - 100

Multiply

More Steps

Evaluate

d \times d^{3} \times 235

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 235

Add the numbers

d^{4} \times 235

Use the commutative property to reorder the terms

235 d^{4}

235 d^{4} - 100

Solution

5 (47 d^{4} - 20)

Show Solution

Find the roots

d_{1} = - \frac{4 20 \times 4 7 ^{3}}{47}, d_{2} = \frac{4 20 \times 4 7 ^{3}}{47}

Alternative Form

d_{1} \approx - 0.807668, d_{2} \approx 0.807668

Evaluate

d \times d^{3} \times 235 - 100

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

d \times d^{3} \times 235 - 100 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 235

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 235

Add the numbers

d^{4} \times 235

Use the commutative property to reorder the terms

235 d^{4}

235 d^{4} - 100 = 0

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

235 d^{4} = 0 + 100

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

235 d^{4} = 100

Divide both sides

\frac{235 d ^{4}}{235} = \frac{100}{235}

Divide the numbers

d^{4} = \frac{100}{235}

Cancel out the common factor 5

d^{4} = \frac{20}{47}

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

d = \pm 4 \frac{20}{47}

Simplify the expression

More Steps

Evaluate

4 \frac{20}{47}

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

\frac{4 20}{4 47}

Multiply by the Conjugate

\frac{4 20 \times 4 4 7 ^{3}}{4 47 \times 4 4 7 ^{3}}

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

\frac{4 20 \times 4 7 ^{3}}{4 47 \times 4 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

447 \times 4 4 7^{3}

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

4 47 \times 4 7^{3}

Calculate the product

4 4 7^{4}

Reduce the index of the radical and exponent with 4

47

\frac{4 20 \times 4 7 ^{3}}{47}

d = \pm \frac{4 20 \times 4 7 ^{3}}{47}

Separate the equation into 2 possible cases

d = \frac{4 20 \times 4 7 ^{3}}{47} d = - \frac{4 20 \times 4 7 ^{3}}{47}

Solution

d_{1} = - \frac{4 20 \times 4 7 ^{3}}{47}, d_{2} = \frac{4 20 \times 4 7 ^{3}}{47}

Alternative Form

d_{1} \approx - 0.807668, d_{2} \approx 0.807668

Show Solution