Solve S^6190-61084

Question

Simplify the expression

190 S^{6} - 61084

Evaluate

S^{6} \times 190 - 61084

Solution

190 S^{6} - 61084

Show Solution

2 (95 S^{6} - 30542)

Evaluate

S^{6} \times 190 - 61084

Use the commutative property to reorder the terms

190 S^{6} - 61084

Solution

2 (95 S^{6} - 30542)

Show Solution

S_{1} = - \frac{6 30542 \times 9 5 ^{5}}{95}, S_{2} = \frac{6 30542 \times 9 5 ^{5}}{95}

Alternative Form

S_{1} \approx - 2.617353, S_{2} \approx 2.617353

Evaluate

S^{6} \times 190 - 61084

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

S^{6} \times 190 - 61084 = 0

Use the commutative property to reorder the terms

190 S^{6} - 61084 = 0

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

190 S^{6} = 0 + 61084

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

190 S^{6} = 61084

Divide both sides

\frac{190 S ^{6}}{190} = \frac{61084}{190}

Divide the numbers

S^{6} = \frac{61084}{190}

Cancel out the common factor 2

S^{6} = \frac{30542}{95}

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

S = \pm 6 \frac{30542}{95}

Simplify the expression

More Steps

Evaluate

6 \frac{30542}{95}

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

\frac{6 30542}{6 95}

Multiply by the Conjugate

\frac{6 30542 \times 6 9 5 ^{5}}{6 95 \times 6 9 5 ^{5}}

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

\frac{6 30542 \times 9 5 ^{5}}{6 95 \times 6 9 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

695 \times 6 9 5^{5}

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

6 95 \times 9 5^{5}

Calculate the product

6 9 5^{6}

Reduce the index of the radical and exponent with 6

95

\frac{6 30542 \times 9 5 ^{5}}{95}

S = \pm \frac{6 30542 \times 9 5 ^{5}}{95}

Separate the equation into 2 possible cases

S = \frac{6 30542 \times 9 5 ^{5}}{95} S = - \frac{6 30542 \times 9 5 ^{5}}{95}

Solution

S_{1} = - \frac{6 30542 \times 9 5 ^{5}}{95}, S_{2} = \frac{6 30542 \times 9 5 ^{5}}{95}

Alternative Form

S_{1} \approx - 2.617353, S_{2} \approx 2.617353

Show Solution