Solve 1c^660-440 - ScanMath

Question

Simplify the expression

60 c^{6} - 440

Evaluate

1 \times c^{6} \times 60 - 440

Solution

More Steps

Evaluate

1 \times c^{6} \times 60

Rewrite the expression

c^{6} \times 60

Use the commutative property to reorder the terms

60 c^{6}

60 c^{6} - 440

Show Solution

Factor the expression

20 (3 c^{6} - 22)

Evaluate

1 \times c^{6} \times 60 - 440

Multiply the terms

More Steps

Evaluate

1 \times c^{6} \times 60

Rewrite the expression

c^{6} \times 60

Use the commutative property to reorder the terms

60 c^{6}

60 c^{6} - 440

Solution

20 (3 c^{6} - 22)

Show Solution

Find the roots

c_{1} = - \frac{6 5346}{3}, c_{2} = \frac{6 5346}{3}

Alternative Form

c_{1} \approx - 1.393853, c_{2} \approx 1.393853

Evaluate

1 \times c^{6} \times 60 - 440

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

1 \times c^{6} \times 60 - 440 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times c^{6} \times 60

Rewrite the expression

c^{6} \times 60

Use the commutative property to reorder the terms

60 c^{6}

60 c^{6} - 440 = 0

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

60 c^{6} = 0 + 440

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

60 c^{6} = 440

Divide both sides

\frac{60 c ^{6}}{60} = \frac{440}{60}

Divide the numbers

c^{6} = \frac{440}{60}

Cancel out the common factor 20

c^{6} = \frac{22}{3}

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

c = \pm 6 \frac{22}{3}

Simplify the expression

More Steps

Evaluate

6 \frac{22}{3}

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

\frac{6 22}{6 3}

Multiply by the Conjugate

\frac{6 22 \times 6 3 ^{5}}{6 3 \times 6 3 ^{5}}

Simplify

\frac{6 22 \times 6 243}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

622 \times 6243

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

6 22 \times 243

Calculate the product

65346

\frac{6 5346}{6 3 \times 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 6 3^{5}

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

6 3 \times 3^{5}

Calculate the product

6 3^{6}

Reduce the index of the radical and exponent with 6

3

\frac{6 5346}{3}

c = \pm \frac{6 5346}{3}

Separate the equation into 2 possible cases

c = \frac{6 5346}{3} c = - \frac{6 5346}{3}

Solution

c_{1} = - \frac{6 5346}{3}, c_{2} = \frac{6 5346}{3}

Alternative Form

c_{1} \approx - 1.393853, c_{2} \approx 1.393853

Show Solution