Solve d^461-34-700

Question

Simplify the expression

61 d^{4} - 734

Evaluate

d^{4} \times 61 - 34 - 700

Use the commutative property to reorder the terms

61 d^{4} - 34 - 700

Solution

61 d^{4} - 734

Show Solution

d_{1} = - \frac{4 734 \times 6 1 ^{3}}{61}, d_{2} = \frac{4 734 \times 6 1 ^{3}}{61}

Alternative Form

d_{1} \approx - 1.86248, d_{2} \approx 1.86248

Evaluate

d^{4} \times 61 - 34 - 700

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

d^{4} \times 61 - 34 - 700 = 0

Use the commutative property to reorder the terms

61 d^{4} - 34 - 700 = 0

Subtract the numbers

61 d^{4} - 734 = 0

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

61 d^{4} = 0 + 734

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

61 d^{4} = 734

Divide both sides

\frac{61 d ^{4}}{61} = \frac{734}{61}

Divide the numbers

d^{4} = \frac{734}{61}

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

d = \pm 4 \frac{734}{61}

Simplify the expression

More Steps

Evaluate

4 \frac{734}{61}

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

\frac{4 734}{4 61}

Multiply by the Conjugate

\frac{4 734 \times 4 6 1 ^{3}}{4 61 \times 4 6 1 ^{3}}

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

\frac{4 734 \times 6 1 ^{3}}{4 61 \times 4 6 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

461 \times 4 6 1^{3}

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

4 61 \times 6 1^{3}

Calculate the product

4 6 1^{4}

Reduce the index of the radical and exponent with 4

61

\frac{4 734 \times 6 1 ^{3}}{61}

d = \pm \frac{4 734 \times 6 1 ^{3}}{61}

Separate the equation into 2 possible cases

d = \frac{4 734 \times 6 1 ^{3}}{61} d = - \frac{4 734 \times 6 1 ^{3}}{61}

Solution

d_{1} = - \frac{4 734 \times 6 1 ^{3}}{61}, d_{2} = \frac{4 734 \times 6 1 ^{3}}{61}

Alternative Form

d_{1} \approx - 1.86248, d_{2} \approx 1.86248

Show Solution