Solve d^605 90/90-21

Question

Simplify the expression

6 d^{6} - 21

Evaluate

d^{6} \times 5 \frac{90}{90} - 21

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{90}{90}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 90 + 90}{90}

Multiply the terms

\frac{450 + 90}{90}

Add the terms

\frac{540}{90}

d^{6} \times \frac{540}{90} - 21

Solution

More Steps

Evaluate

1 \times \frac{540}{90}

Any expression multiplied by 1 remains the same

\frac{540}{90}

Reduce the fraction

6

6 d^{6} - 21

Show Solution

Factor the expression

3 (2 d^{6} - 7)

Evaluate

d^{6} \times 5 \frac{90}{90} - 21

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{90}{90}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 90 + 90}{90}

Multiply the terms

\frac{450 + 90}{90}

Add the terms

\frac{540}{90}

d^{6} \times \frac{540}{90} - 21

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{540}{90}

Any expression multiplied by 1 remains the same

\frac{540}{90}

Reduce the fraction

6

Evaluate

6 d^{6}

6 d^{6} - 21

Solution

3 (2 d^{6} - 7)

Show Solution

Find the roots

d_{1} = - \frac{6 224}{2}, d_{2} = \frac{6 224}{2}

Alternative Form

d_{1} \approx - 1.232191, d_{2} \approx 1.232191

Evaluate

d^{6} \times 5 \frac{90}{90} - 21

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

d^{6} \times 5 \frac{90}{90} - 21 = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{90}{90}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 90 + 90}{90}

Multiply the terms

\frac{450 + 90}{90}

Add the terms

\frac{540}{90}

d^{6} \times \frac{540}{90} - 21 = 0

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{540}{90}

Any expression multiplied by 1 remains the same

\frac{540}{90}

Reduce the fraction

6

6 d^{6} - 21 = 0

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

6 d^{6} = 0 + 21

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

6 d^{6} = 21

Divide both sides

\frac{6 d ^{6}}{6} = \frac{21}{6}

Divide the numbers

d^{6} = \frac{21}{6}

Cancel out the common factor 3

d^{6} = \frac{7}{2}

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

d = \pm 6 \frac{7}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{7}{2}

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

\frac{6 7}{6 2}

Multiply by the Conjugate

\frac{6 7 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 7 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 632

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

6 7 \times 32

Calculate the product

6224

\frac{6 224}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 6 2^{5}

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

6 2 \times 2^{5}

Calculate the product

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 224}{2}

d = \pm \frac{6 224}{2}

Separate the equation into 2 possible cases

d = \frac{6 224}{2} d = - \frac{6 224}{2}

Solution

d_{1} = - \frac{6 224}{2}, d_{2} = \frac{6 224}{2}

Alternative Form

d_{1} \approx - 1.232191, d_{2} \approx 1.232191

Show Solution