Solve r---r^584 - ScanMath

Question

Simplify the expression

r - 84 r^{5}

Evaluate

r - r^{5} \times 84

Solution

r - 84 r^{5}

Show Solution

r (1 - 84 r^{4})

Evaluate

r - r^{5} \times 84

Use the commutative property to reorder the terms

r - 84 r^{5}

Rewrite the expression

r - r \times 84 r^{4}

Solution

r (1 - 84 r^{4})

Show Solution

r_{1} = - \frac{4 8 4 ^{3}}{84}, r_{2} = 0, r_{3} = \frac{4 8 4 ^{3}}{84}

Alternative Form

r_{1} \approx - 0.330316, r_{2} = 0, r_{3} \approx 0.330316

Evaluate

r - r^{5} \times 84

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

r - r^{5} \times 84 = 0

Use the commutative property to reorder the terms

r - 84 r^{5} = 0

Factor the expression

r (1 - 84 r^{4}) = 0

Separate the equation into 2 possible cases

r = 0 1 - 84 r^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 84 r^{4} = 0

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

- 84 r^{4} = 0 - 1

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

- 84 r^{4} = - 1

Change the signs on both sides of the equation

84 r^{4} = 1

Divide both sides

\frac{84 r ^{4}}{84} = \frac{1}{84}

Divide the numbers

r^{4} = \frac{1}{84}

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

r = \pm 4 \frac{1}{84}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{84}

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

\frac{4 1}{4 84}

Simplify the radical expression

\frac{1}{4 84}

Multiply by the Conjugate

\frac{4 8 4 ^{3}}{4 84 \times 4 8 4 ^{3}}

Multiply the numbers

\frac{4 8 4 ^{3}}{84}

r = \pm \frac{4 8 4 ^{3}}{84}

Separate the equation into 2 possible cases

r = \frac{4 8 4 ^{3}}{84} r = - \frac{4 8 4 ^{3}}{84}

r = 0 r = \frac{4 8 4 ^{3}}{84} r = - \frac{4 8 4 ^{3}}{84}

Solution

r_{1} = - \frac{4 8 4 ^{3}}{84}, r_{2} = 0, r_{3} = \frac{4 8 4 ^{3}}{84}

Alternative Form

r_{1} \approx - 0.330316, r_{2} = 0, r_{3} \approx 0.330316

Show Solution