Solve dd^37-2021 - ScanMath

Question

Simplify the expression

7 d^{4} - 2021

Evaluate

d \times d^{3} \times 7 - 2021

Solution

More Steps

Evaluate

d \times d^{3} \times 7

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 7

Add the numbers

d^{4} \times 7

Use the commutative property to reorder the terms

7 d^{4}

7 d^{4} - 2021

Show Solution

d_{1} = - \frac{4 693203}{7}, d_{2} = \frac{4 693203}{7}

Alternative Form

d_{1} \approx - 4.122086, d_{2} \approx 4.122086

Evaluate

d \times d^{3} \times 7 - 2021

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

d \times d^{3} \times 7 - 2021 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 7

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 7

Add the numbers

d^{4} \times 7

Use the commutative property to reorder the terms

7 d^{4}

7 d^{4} - 2021 = 0

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

7 d^{4} = 0 + 2021

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

7 d^{4} = 2021

Divide both sides

\frac{7 d ^{4}}{7} = \frac{2021}{7}

Divide the numbers

d^{4} = \frac{2021}{7}

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

d = \pm 4 \frac{2021}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{2021}{7}

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

\frac{4 2021}{4 7}

Multiply by the Conjugate

\frac{4 2021 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 2021 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

42021 \times 4343

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

4 2021 \times 343

Calculate the product

4693203

\frac{4 693203}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 693203}{7}

d = \pm \frac{4 693203}{7}

Separate the equation into 2 possible cases

d = \frac{4 693203}{7} d = - \frac{4 693203}{7}

Solution

d_{1} = - \frac{4 693203}{7}, d_{2} = \frac{4 693203}{7}

Alternative Form

d_{1} \approx - 4.122086, d_{2} \approx 4.122086

Show Solution