Solve dd^5635-10 - ScanMath

Question

Simplify the expression

635 d^{6} - 10

Evaluate

d \times d^{5} \times 635 - 10

Solution

More Steps

Evaluate

d \times d^{5} \times 635

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 635

Add the numbers

d^{6} \times 635

Use the commutative property to reorder the terms

635 d^{6}

635 d^{6} - 10

Show Solution

Factor the expression

5 (127 d^{6} - 2)

Evaluate

d \times d^{5} \times 635 - 10

Multiply

More Steps

Evaluate

d \times d^{5} \times 635

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 635

Add the numbers

d^{6} \times 635

Use the commutative property to reorder the terms

635 d^{6}

635 d^{6} - 10

Solution

5 (127 d^{6} - 2)

Show Solution

Find the roots

d_{1} = - \frac{6 2 \times 12 7 ^{5}}{127}, d_{2} = \frac{6 2 \times 12 7 ^{5}}{127}

Alternative Form

d_{1} \approx - 0.500654, d_{2} \approx 0.500654

Evaluate

d \times d^{5} \times 635 - 10

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

d \times d^{5} \times 635 - 10 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 635

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 635

Add the numbers

d^{6} \times 635

Use the commutative property to reorder the terms

635 d^{6}

635 d^{6} - 10 = 0

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

635 d^{6} = 0 + 10

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

635 d^{6} = 10

Divide both sides

\frac{635 d ^{6}}{635} = \frac{10}{635}

Divide the numbers

d^{6} = \frac{10}{635}

Cancel out the common factor 5

d^{6} = \frac{2}{127}

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

d = \pm 6 \frac{2}{127}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{127}

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

\frac{6 2}{6 127}

Multiply by the Conjugate

\frac{6 2 \times 6 12 7 ^{5}}{6 127 \times 6 12 7 ^{5}}

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

\frac{6 2 \times 12 7 ^{5}}{6 127 \times 6 12 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

6127 \times 6 12 7^{5}

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

6 127 \times 12 7^{5}

Calculate the product

6 12 7^{6}

Reduce the index of the radical and exponent with 6

127

\frac{6 2 \times 12 7 ^{5}}{127}

d = \pm \frac{6 2 \times 12 7 ^{5}}{127}

Separate the equation into 2 possible cases

d = \frac{6 2 \times 12 7 ^{5}}{127} d = - \frac{6 2 \times 12 7 ^{5}}{127}

Solution

d_{1} = - \frac{6 2 \times 12 7 ^{5}}{127}, d_{2} = \frac{6 2 \times 12 7 ^{5}}{127}

Alternative Form

d_{1} \approx - 0.500654, d_{2} \approx 0.500654

Show Solution