Solve d^455-6-200

Question

Simplify the expression

55 d^{4} - 206

Evaluate

d^{4} \times 55 - 6 - 200

Use the commutative property to reorder the terms

55 d^{4} - 6 - 200

Solution

55 d^{4} - 206

Show Solution

d_{1} = - \frac{4 206 \times 5 5 ^{3}}{55}, d_{2} = \frac{4 206 \times 5 5 ^{3}}{55}

Alternative Form

d_{1} \approx - 1.391157, d_{2} \approx 1.391157

Evaluate

d^{4} \times 55 - 6 - 200

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

d^{4} \times 55 - 6 - 200 = 0

Use the commutative property to reorder the terms

55 d^{4} - 6 - 200 = 0

Subtract the numbers

55 d^{4} - 206 = 0

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

55 d^{4} = 0 + 206

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

55 d^{4} = 206

Divide both sides

\frac{55 d ^{4}}{55} = \frac{206}{55}

Divide the numbers

d^{4} = \frac{206}{55}

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

d = \pm 4 \frac{206}{55}

Simplify the expression

More Steps

Evaluate

4 \frac{206}{55}

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

\frac{4 206}{4 55}

Multiply by the Conjugate

\frac{4 206 \times 4 5 5 ^{3}}{4 55 \times 4 5 5 ^{3}}

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

\frac{4 206 \times 5 5 ^{3}}{4 55 \times 4 5 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

455 \times 4 5 5^{3}

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

4 55 \times 5 5^{3}

Calculate the product

4 5 5^{4}

Reduce the index of the radical and exponent with 4

55

\frac{4 206 \times 5 5 ^{3}}{55}

d = \pm \frac{4 206 \times 5 5 ^{3}}{55}

Separate the equation into 2 possible cases

d = \frac{4 206 \times 5 5 ^{3}}{55} d = - \frac{4 206 \times 5 5 ^{3}}{55}

Solution

d_{1} = - \frac{4 206 \times 5 5 ^{3}}{55}, d_{2} = \frac{4 206 \times 5 5 ^{3}}{55}

Alternative Form

d_{1} \approx - 1.391157, d_{2} \approx 1.391157

Show Solution