Solve d^65-1009-2

Question

Simplify the expression

5 d^{6} - 1011

Evaluate

d^{6} \times 5 - 1009 - 2

Use the commutative property to reorder the terms

5 d^{6} - 1009 - 2

Solution

5 d^{6} - 1011

Show Solution

d_{1} = - \frac{6 3159375}{5}, d_{2} = \frac{6 3159375}{5}

Alternative Form

d_{1} \approx - 2.422684, d_{2} \approx 2.422684

Evaluate

d^{6} \times 5 - 1009 - 2

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

d^{6} \times 5 - 1009 - 2 = 0

Use the commutative property to reorder the terms

5 d^{6} - 1009 - 2 = 0

Subtract the numbers

5 d^{6} - 1011 = 0

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

5 d^{6} = 0 + 1011

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

5 d^{6} = 1011

Divide both sides

\frac{5 d ^{6}}{5} = \frac{1011}{5}

Divide the numbers

d^{6} = \frac{1011}{5}

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

d = \pm 6 \frac{1011}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{1011}{5}

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

\frac{6 1011}{6 5}

Multiply by the Conjugate

\frac{6 1011 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{6 1011 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

61011 \times 63125

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

6 1011 \times 3125

Calculate the product

63159375

\frac{6 3159375}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{6 3159375}{5}

d = \pm \frac{6 3159375}{5}

Separate the equation into 2 possible cases

d = \frac{6 3159375}{5} d = - \frac{6 3159375}{5}

Solution

d_{1} = - \frac{6 3159375}{5}, d_{2} = \frac{6 3159375}{5}

Alternative Form

d_{1} \approx - 2.422684, d_{2} \approx 2.422684

Show Solution