Solve s^64-1197-1084

Question

Simplify the expression

4 s^{6} - 2281

Evaluate

s^{6} \times 4 - 1197 - 1084

Use the commutative property to reorder the terms

4 s^{6} - 1197 - 1084

Solution

4 s^{6} - 2281

Show Solution

s_{1} = - \frac{6 36496}{2}, s_{2} = \frac{6 36496}{2}

Alternative Form

s_{1} \approx - 2.87968, s_{2} \approx 2.87968

Evaluate

s^{6} \times 4 - 1197 - 1084

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

s^{6} \times 4 - 1197 - 1084 = 0

Use the commutative property to reorder the terms

4 s^{6} - 1197 - 1084 = 0

Subtract the numbers

4 s^{6} - 2281 = 0

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

4 s^{6} = 0 + 2281

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

4 s^{6} = 2281

Divide both sides

\frac{4 s ^{6}}{4} = \frac{2281}{4}

Divide the numbers

s^{6} = \frac{2281}{4}

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

s = \pm 6 \frac{2281}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{2281}{4}

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

\frac{6 2281}{6 4}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{6 2281}{3 2}

Multiply by the Conjugate

\frac{6 2281 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{6 2281 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

62281 \times 34

Use n a = mn a^{m} to expand the expression

62281 \times 6 4^{2}

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

6 2281 \times 4^{2}

Calculate the product

636496

\frac{6 36496}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{6 36496}{2}

s = \pm \frac{6 36496}{2}

Separate the equation into 2 possible cases

s = \frac{6 36496}{2} s = - \frac{6 36496}{2}

Solution

s_{1} = - \frac{6 36496}{2}, s_{2} = \frac{6 36496}{2}

Alternative Form

s_{1} \approx - 2.87968, s_{2} \approx 2.87968

Show Solution