Solve d^455-5-200

Question

Simplify the expression

55 d^{4} - 205

Evaluate

d^{4} \times 55 - 5 - 200

Use the commutative property to reorder the terms

55 d^{4} - 5 - 200

Solution

55 d^{4} - 205

Show Solution

5 (11 d^{4} - 41)

Evaluate

d^{4} \times 55 - 5 - 200

Use the commutative property to reorder the terms

55 d^{4} - 5 - 200

Subtract the numbers

55 d^{4} - 205

Solution

5 (11 d^{4} - 41)

Show Solution

d_{1} = - \frac{4 54571}{11}, d_{2} = \frac{4 54571}{11}

Alternative Form

d_{1} \approx - 1.389466, d_{2} \approx 1.389466

Evaluate

d^{4} \times 55 - 5 - 200

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

d^{4} \times 55 - 5 - 200 = 0

Use the commutative property to reorder the terms

55 d^{4} - 5 - 200 = 0

Subtract the numbers

55 d^{4} - 205 = 0

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

55 d^{4} = 0 + 205

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

55 d^{4} = 205

Divide both sides

\frac{55 d ^{4}}{55} = \frac{205}{55}

Divide the numbers

d^{4} = \frac{205}{55}

Cancel out the common factor 5

d^{4} = \frac{41}{11}

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

d = \pm 4 \frac{41}{11}

Simplify the expression

More Steps

Evaluate

4 \frac{41}{11}

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

\frac{4 41}{4 11}

Multiply by the Conjugate

\frac{4 41 \times 4 1 1 ^{3}}{4 11 \times 4 1 1 ^{3}}

Simplify

\frac{4 41 \times 4 1331}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

441 \times 41331

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

4 41 \times 1331

Calculate the product

454571

\frac{4 54571}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

411 \times 4 1 1^{3}

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

4 11 \times 1 1^{3}

Calculate the product

4 1 1^{4}

Reduce the index of the radical and exponent with 4

11

\frac{4 54571}{11}

d = \pm \frac{4 54571}{11}

Separate the equation into 2 possible cases

d = \frac{4 54571}{11} d = - \frac{4 54571}{11}

Solution

d_{1} = - \frac{4 54571}{11}, d_{2} = \frac{4 54571}{11}

Alternative Form

d_{1} \approx - 1.389466, d_{2} \approx 1.389466

Show Solution