Solve r^5522-r6 - ScanMath

Question

Simplify the expression

Solution

522 r^{5} - 6 r

Evaluate

r^{5} \times 522 - r \times 6

Use the commutative property to reorder the terms

522 r^{5} - r \times 6

Solution

522 r^{5} - 6 r

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Factor

6 r (87 r^{4} - 1)

Evaluate

r^{5} \times 522 - r \times 6

Use the commutative property to reorder the terms

522 r^{5} - r \times 6

Use the commutative property to reorder the terms

522 r^{5} - 6 r

Rewrite the expression

6 r \times 87 r^{4} - 6 r

Solution

6 r (87 r^{4} - 1)

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Find the roots of the algebra expression

r_{1} = - \frac{4 8 7 ^{3}}{87}, r_{2} = 0, r_{3} = \frac{4 8 7 ^{3}}{87}

Alternative Form

r_{1} \approx - 0.327431, r_{2} = 0, r_{3} \approx 0.327431

Evaluate

r^{5} \times 522 - r \times 6

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

r^{5} \times 522 - r \times 6 = 0

Use the commutative property to reorder the terms

522 r^{5} - r \times 6 = 0

Use the commutative property to reorder the terms

522 r^{5} - 6 r = 0

Factor the expression

6 r (87 r^{4} - 1) = 0

Divide both sides

r (87 r^{4} - 1) = 0

Separate the equation into 2 possible cases

r = 0 87 r^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

87 r^{4} - 1 = 0

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

87 r^{4} = 0 + 1

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

87 r^{4} = 1

Divide both sides

\frac{87 r ^{4}}{87} = \frac{1}{87}

Divide the numbers

r^{4} = \frac{1}{87}

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

r = \pm 4 \frac{1}{87}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{87}

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

\frac{4 1}{4 87}

Simplify the radical expression

\frac{1}{4 87}

Multiply by the Conjugate

\frac{4 8 7 ^{3}}{4 87 \times 4 8 7 ^{3}}

Multiply the numbers

\frac{4 8 7 ^{3}}{87}

r = \pm \frac{4 8 7 ^{3}}{87}

Separate the equation into 2 possible cases

r = \frac{4 8 7 ^{3}}{87} r = - \frac{4 8 7 ^{3}}{87}

r = 0 r = \frac{4 8 7 ^{3}}{87} r = - \frac{4 8 7 ^{3}}{87}

Solution

r_{1} = - \frac{4 8 7 ^{3}}{87}, r_{2} = 0, r_{3} = \frac{4 8 7 ^{3}}{87}

Alternative Form

r_{1} \approx - 0.327431, r_{2} = 0, r_{3} \approx 0.327431

Show Solution