Solve dd^324-315 - ScanMath

Question

Simplify the expression

24 d^{4} - 315

Evaluate

d \times d^{3} \times 24 - 315

Solution

More Steps

Evaluate

d \times d^{3} \times 24

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 24

Add the numbers

d^{4} \times 24

Use the commutative property to reorder the terms

24 d^{4}

24 d^{4} - 315

Show Solution

Factor the expression

3 (8 d^{4} - 105)

Evaluate

d \times d^{3} \times 24 - 315

Multiply

More Steps

Evaluate

d \times d^{3} \times 24

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 24

Add the numbers

d^{4} \times 24

Use the commutative property to reorder the terms

24 d^{4}

24 d^{4} - 315

Solution

3 (8 d^{4} - 105)

Show Solution

Find the roots

d_{1} = - \frac{4 210}{2}, d_{2} = \frac{4 210}{2}

Alternative Form

d_{1} \approx - 1.903377, d_{2} \approx 1.903377

Evaluate

d \times d^{3} \times 24 - 315

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

d \times d^{3} \times 24 - 315 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 24

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 24

Add the numbers

d^{4} \times 24

Use the commutative property to reorder the terms

24 d^{4}

24 d^{4} - 315 = 0

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

24 d^{4} = 0 + 315

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

24 d^{4} = 315

Divide both sides

\frac{24 d ^{4}}{24} = \frac{315}{24}

Divide the numbers

d^{4} = \frac{315}{24}

Cancel out the common factor 3

d^{4} = \frac{105}{8}

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

d = \pm 4 \frac{105}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{105}{8}

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

\frac{4 105}{4 8}

Multiply by the Conjugate

\frac{4 105 \times 4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{4 105 \times 2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

4105 \times 2^{2} 42

Multiply the terms

4210 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 4210

\frac{2 ^{2} 4 210}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4 8^{3}

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

4 8 \times 8^{3}

Calculate the product

4 8^{4}

Transform the expression

4 2^{12}

Reduce the index of the radical and exponent with 4

2^{3}

\frac{2 ^{2} 4 210}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{4 210}{2}

d = \pm \frac{4 210}{2}

Separate the equation into 2 possible cases

d = \frac{4 210}{2} d = - \frac{4 210}{2}

Solution

d_{1} = - \frac{4 210}{2}, d_{2} = \frac{4 210}{2}

Alternative Form

d_{1} \approx - 1.903377, d_{2} \approx 1.903377

Show Solution