Solve d^652-39-40

Question

Simplify the expression

52 d^{6} - 79

Evaluate

d^{6} \times 52 - 39 - 40

Use the commutative property to reorder the terms

52 d^{6} - 39 - 40

Solution

52 d^{6} - 79

Show Solution

d_{1} = - \frac{6 79 \times 5 2 ^{5}}{52}, d_{2} = \frac{6 79 \times 5 2 ^{5}}{52}

Alternative Form

d_{1} \approx - 1.072187, d_{2} \approx 1.072187

Evaluate

d^{6} \times 52 - 39 - 40

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

d^{6} \times 52 - 39 - 40 = 0

Use the commutative property to reorder the terms

52 d^{6} - 39 - 40 = 0

Subtract the numbers

52 d^{6} - 79 = 0

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

52 d^{6} = 0 + 79

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

52 d^{6} = 79

Divide both sides

\frac{52 d ^{6}}{52} = \frac{79}{52}

Divide the numbers

d^{6} = \frac{79}{52}

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

d = \pm 6 \frac{79}{52}

Simplify the expression

More Steps

Evaluate

6 \frac{79}{52}

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

\frac{6 79}{6 52}

Multiply by the Conjugate

\frac{6 79 \times 6 5 2 ^{5}}{6 52 \times 6 5 2 ^{5}}

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

\frac{6 79 \times 5 2 ^{5}}{6 52 \times 6 5 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

652 \times 6 5 2^{5}

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

6 52 \times 5 2^{5}

Calculate the product

6 5 2^{6}

Reduce the index of the radical and exponent with 6

52

\frac{6 79 \times 5 2 ^{5}}{52}

d = \pm \frac{6 79 \times 5 2 ^{5}}{52}

Separate the equation into 2 possible cases

d = \frac{6 79 \times 5 2 ^{5}}{52} d = - \frac{6 79 \times 5 2 ^{5}}{52}

Solution

d_{1} = - \frac{6 79 \times 5 2 ^{5}}{52}, d_{2} = \frac{6 79 \times 5 2 ^{5}}{52}

Alternative Form

d_{1} \approx - 1.072187, d_{2} \approx 1.072187

Show Solution