Solve c^6240-10240010

Question

Simplify the expression

240 c^{6} - 10240010

Evaluate

c^{6} \times 240 - 10240010

Solution

240 c^{6} - 10240010

Show Solution

10 (24 c^{6} - 1024001)

Evaluate

c^{6} \times 240 - 10240010

Use the commutative property to reorder the terms

240 c^{6} - 10240010

Solution

10 (24 c^{6} - 1024001)

Show Solution

c_{1} = - \frac{6 1024001 \times 2 4 ^{5}}{24}, c_{2} = \frac{6 1024001 \times 2 4 ^{5}}{24}

Alternative Form

c_{1} \approx - 5.91128, c_{2} \approx 5.91128

Evaluate

c^{6} \times 240 - 10240010

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

c^{6} \times 240 - 10240010 = 0

Use the commutative property to reorder the terms

240 c^{6} - 10240010 = 0

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

240 c^{6} = 0 + 10240010

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

240 c^{6} = 10240010

Divide both sides

\frac{240 c ^{6}}{240} = \frac{10240010}{240}

Divide the numbers

c^{6} = \frac{10240010}{240}

Cancel out the common factor 10

c^{6} = \frac{1024001}{24}

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

c = \pm 6 \frac{1024001}{24}

Simplify the expression

More Steps

Evaluate

6 \frac{1024001}{24}

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

\frac{6 1024001}{6 24}

Multiply by the Conjugate

\frac{6 1024001 \times 6 2 4 ^{5}}{6 24 \times 6 2 4 ^{5}}

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

\frac{6 1024001 \times 2 4 ^{5}}{6 24 \times 6 2 4 ^{5}}

Multiply the numbers

More Steps

Evaluate

624 \times 6 2 4^{5}

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

6 24 \times 2 4^{5}

Calculate the product

6 2 4^{6}

Reduce the index of the radical and exponent with 6

24

\frac{6 1024001 \times 2 4 ^{5}}{24}

c = \pm \frac{6 1024001 \times 2 4 ^{5}}{24}

Separate the equation into 2 possible cases

c = \frac{6 1024001 \times 2 4 ^{5}}{24} c = - \frac{6 1024001 \times 2 4 ^{5}}{24}

Solution

c_{1} = - \frac{6 1024001 \times 2 4 ^{5}}{24}, c_{2} = \frac{6 1024001 \times 2 4 ^{5}}{24}

Alternative Form

c_{1} \approx - 5.91128, c_{2} \approx 5.91128

Show Solution