Solve d^605 130/90-17

Question

d^{6} \times 5 \frac{130}{90} - 17

Simplify the expression

\frac{58}{9} d^{6} - 17

Evaluate

d^{6} \times 5 \frac{130}{90} - 17

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{130}{90}

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

\frac{5 \times 90 + 130}{90}

Multiply the terms

\frac{450 + 130}{90}

Add the terms

\frac{580}{90}

d^{6} \times \frac{580}{90} - 17

Solution

More Steps

Evaluate

1 \times \frac{580}{90}

Any expression multiplied by 1 remains the same

\frac{580}{90}

Reduce the fraction

\frac{58}{9}

\frac{58}{9} d^{6} - 17

Show Solution

Factor the expression

\frac{1}{9} (58 d^{6} - 153)

Evaluate

d^{6} \times 5 \frac{130}{90} - 17

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{130}{90}

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

\frac{5 \times 90 + 130}{90}

Multiply the terms

\frac{450 + 130}{90}

Add the terms

\frac{580}{90}

d^{6} \times \frac{580}{90} - 17

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{580}{90}

Any expression multiplied by 1 remains the same

\frac{580}{90}

Reduce the fraction

\frac{58}{9}

Evaluate

\frac{58}{9} d^{6}

\frac{58}{9} d^{6} - 17

Solution

\frac{1}{9} (58 d^{6} - 153)

Show Solution

Find the roots

d_{1} = - \frac{6 153 \times 5 8 ^{5}}{58}, d_{2} = \frac{6 153 \times 5 8 ^{5}}{58}

Alternative Form

d_{1} \approx - 1.175467, d_{2} \approx 1.175467

Evaluate

d^{6} \times 5 \frac{130}{90} - 17

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

d^{6} \times 5 \frac{130}{90} - 17 = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{130}{90}

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

\frac{5 \times 90 + 130}{90}

Multiply the terms

\frac{450 + 130}{90}

Add the terms

\frac{580}{90}

d^{6} \times \frac{580}{90} - 17 = 0

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{580}{90}

Any expression multiplied by 1 remains the same

\frac{580}{90}

Reduce the fraction

\frac{58}{9}

\frac{58}{9} d^{6} - 17 = 0

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

\frac{58}{9} d^{6} = 0 + 17

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

\frac{58}{9} d^{6} = 17

Multiply by the reciprocal

\frac{58}{9} d^{6} \times \frac{9}{58} = 17 \times \frac{9}{58}

Multiply

d^{6} = 17 \times \frac{9}{58}

Multiply

More Steps

Evaluate

17 \times \frac{9}{58}

Multiply the numbers

\frac{17 \times 9}{58}

Multiply the numbers

\frac{153}{58}

d^{6} = \frac{153}{58}

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

d = \pm 6 \frac{153}{58}

Simplify the expression

More Steps

Evaluate

6 \frac{153}{58}

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

\frac{6 153}{6 58}

Multiply by the Conjugate

\frac{6 153 \times 6 5 8 ^{5}}{6 58 \times 6 5 8 ^{5}}

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

\frac{6 153 \times 5 8 ^{5}}{6 58 \times 6 5 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

658 \times 6 5 8^{5}

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

6 58 \times 5 8^{5}

Calculate the product

6 5 8^{6}

Reduce the index of the radical and exponent with 6

58

\frac{6 153 \times 5 8 ^{5}}{58}

d = \pm \frac{6 153 \times 5 8 ^{5}}{58}

Separate the equation into 2 possible cases

d = \frac{6 153 \times 5 8 ^{5}}{58} d = - \frac{6 153 \times 5 8 ^{5}}{58}

Solution

d_{1} = - \frac{6 153 \times 5 8 ^{5}}{58}, d_{2} = \frac{6 153 \times 5 8 ^{5}}{58}

Alternative Form

d_{1} \approx - 1.175467, d_{2} \approx 1.175467

Show Solution