Solve 2015 c^630-60 - Socratic AI (ScanMath)

Question

Simplify the expression

60450 c^{6} - 60

Evaluate

2015 c^{6} \times 30 - 60

Solution

60450 c^{6} - 60

Show Solution

30 (2015 c^{6} - 2)

Evaluate

2015 c^{6} \times 30 - 60

Multiply the terms

60450 c^{6} - 60

Solution

30 (2015 c^{6} - 2)

Show Solution

c_{1} = - \frac{6 2 \times 201 5 ^{5}}{2015}, c_{2} = \frac{6 2 \times 201 5 ^{5}}{2015}

Alternative Form

c_{1} \approx - 0.315834, c_{2} \approx 0.315834

Evaluate

2015 c^{6} \times 30 - 60

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

2015 c^{6} \times 30 - 60 = 0

Multiply the terms

60450 c^{6} - 60 = 0

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

60450 c^{6} = 0 + 60

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

60450 c^{6} = 60

Divide both sides

\frac{60450 c ^{6}}{60450} = \frac{60}{60450}

Divide the numbers

c^{6} = \frac{60}{60450}

Cancel out the common factor 30

c^{6} = \frac{2}{2015}

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

c = \pm 6 \frac{2}{2015}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{2015}

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

\frac{6 2}{6 2015}

Multiply by the Conjugate

\frac{6 2 \times 6 201 5 ^{5}}{6 2015 \times 6 201 5 ^{5}}

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

\frac{6 2 \times 201 5 ^{5}}{6 2015 \times 6 201 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

62015 \times 6 201 5^{5}

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

6 2015 \times 201 5^{5}

Calculate the product

6 201 5^{6}

Reduce the index of the radical and exponent with 6

2015

\frac{6 2 \times 201 5 ^{5}}{2015}

c = \pm \frac{6 2 \times 201 5 ^{5}}{2015}

Separate the equation into 2 possible cases

c = \frac{6 2 \times 201 5 ^{5}}{2015} c = - \frac{6 2 \times 201 5 ^{5}}{2015}

Solution

c_{1} = - \frac{6 2 \times 201 5 ^{5}}{2015}, c_{2} = \frac{6 2 \times 201 5 ^{5}}{2015}

Alternative Form

c_{1} \approx - 0.315834, c_{2} \approx 0.315834

Show Solution