Solve s-3s^6105s - ScanMath

Question

Simplify the expression

s - 315 s^{7}

Evaluate

s - 3 s^{6} \times 105 s

Solution

More Steps

Evaluate

3 s^{6} \times 105 s

Multiply the terms

315 s^{6} \times s

Multiply the terms with the same base by adding their exponents

315 s^{6 + 1}

Add the numbers

315 s^{7}

s - 315 s^{7}

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Factor the expression

s (1 - 315 s^{6})

Evaluate

s - 3 s^{6} \times 105 s

Multiply

More Steps

Evaluate

3 s^{6} \times 105 s

Multiply the terms

315 s^{6} \times s

Multiply the terms with the same base by adding their exponents

315 s^{6 + 1}

Add the numbers

315 s^{7}

s - 315 s^{7}

Rewrite the expression

s - s \times 315 s^{6}

Solution

s (1 - 315 s^{6})

Show Solution

Find the roots

s_{1} = - \frac{6 31 5 ^{5}}{315}, s_{2} = 0, s_{3} = \frac{6 31 5 ^{5}}{315}

Alternative Form

s_{1} \approx - 0.383367, s_{2} = 0, s_{3} \approx 0.383367

Evaluate

s - 3 s^{6} \times 105 s

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

s - 3 s^{6} \times 105 s = 0

Multiply

More Steps

Multiply the terms

3 s^{6} \times 105 s

Multiply the terms

315 s^{6} \times s

Multiply the terms with the same base by adding their exponents

315 s^{6 + 1}

Add the numbers

315 s^{7}

s - 315 s^{7} = 0

Factor the expression

s (1 - 315 s^{6}) = 0

Separate the equation into 2 possible cases

s = 0 1 - 315 s^{6} = 0

Solve the equation

More Steps

Evaluate

1 - 315 s^{6} = 0

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

- 315 s^{6} = 0 - 1

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

- 315 s^{6} = - 1

Change the signs on both sides of the equation

315 s^{6} = 1

Divide both sides

\frac{315 s ^{6}}{315} = \frac{1}{315}

Divide the numbers

s^{6} = \frac{1}{315}

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

s = \pm 6 \frac{1}{315}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{315}

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

\frac{6 1}{6 315}

Simplify the radical expression

\frac{1}{6 315}

Multiply by the Conjugate

\frac{6 31 5 ^{5}}{6 315 \times 6 31 5 ^{5}}

Multiply the numbers

\frac{6 31 5 ^{5}}{315}

s = \pm \frac{6 31 5 ^{5}}{315}

Separate the equation into 2 possible cases

s = \frac{6 31 5 ^{5}}{315} s = - \frac{6 31 5 ^{5}}{315}

s = 0 s = \frac{6 31 5 ^{5}}{315} s = - \frac{6 31 5 ^{5}}{315}

Solution

s_{1} = - \frac{6 31 5 ^{5}}{315}, s_{2} = 0, s_{3} = \frac{6 31 5 ^{5}}{315}

Alternative Form

s_{1} \approx - 0.383367, s_{2} = 0, s_{3} \approx 0.383367

Show Solution