Solve -3r^29r^4=-5r^2

Question

Solve the equation

r_{1} = - \frac{4 15}{3}, r_{2} = 0, r_{3} = \frac{4 15}{3}

Alternative Form

r_{1} \approx - 0.655997, r_{2} = 0, r_{3} \approx 0.655997

Evaluate

- 3 r^{2} \times 9 r^{4} = - 5 r^{2}

Multiply

More Steps

Evaluate

- 3 r^{2} \times 9 r^{4}

Multiply the terms

- 27 r^{2} \times r^{4}

Multiply the terms with the same base by adding their exponents

- 27 r^{2 + 4}

Add the numbers

- 27 r^{6}

- 27 r^{6} = - 5 r^{2}

Add or subtract both sides

- 27 r^{6} - (- 5 r^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 27 r^{6} + 5 r^{2} = 0

Factor the expression

r^{2} (- 27 r^{4} + 5) = 0

Separate the equation into 2 possible cases

r^{2} = 0 - 27 r^{4} + 5 = 0

The only way a power can be 0 is when the base equals 0

r = 0 - 27 r^{4} + 5 = 0

Solve the equation

More Steps

Evaluate

- 27 r^{4} + 5 = 0

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

- 27 r^{4} = 0 - 5

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

- 27 r^{4} = - 5

Change the signs on both sides of the equation

27 r^{4} = 5

Divide both sides

\frac{27 r ^{4}}{27} = \frac{5}{27}

Divide the numbers

r^{4} = \frac{5}{27}

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

r = \pm 4 \frac{5}{27}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{27}

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

\frac{4 5}{4 27}

Multiply by the Conjugate

\frac{4 5 \times 4 2 7 ^{3}}{4 27 \times 4 2 7 ^{3}}

Simplify

\frac{4 5 \times 3 ^{2} 4 3}{4 27 \times 4 2 7 ^{3}}

Multiply the numbers

\frac{3 ^{2} 4 15}{4 27 \times 4 2 7 ^{3}}

Multiply the numbers

\frac{3 ^{2} 4 15}{3 ^{3}}

Reduce the fraction

\frac{4 15}{3}

r = \pm \frac{4 15}{3}

Separate the equation into 2 possible cases

r = \frac{4 15}{3} r = - \frac{4 15}{3}

r = 0 r = \frac{4 15}{3} r = - \frac{4 15}{3}

Solution

r_{1} = - \frac{4 15}{3}, r_{2} = 0, r_{3} = \frac{4 15}{3}

Alternative Form

r_{1} \approx - 0.655997, r_{2} = 0, r_{3} \approx 0.655997

Show Solution

Rewrite the equation

- 27 x^{6} - 81 x^{4} y^{2} - 81 x^{2} y^{4} - 27 y^{6} + 5 x^{2} + 5 y^{2} = 0

Evaluate

- 3 r^{2} \times 9 r^{4} = - 5 r^{2}

Evaluate

More Steps

Evaluate

- 3 r^{2} \times 9 r^{4}

Multiply the terms

- 27 r^{2} \times r^{4}

Multiply the terms with the same base by adding their exponents

- 27 r^{2 + 4}

Add the numbers

- 27 r^{6}

- 27 r^{6} = - 5 r^{2}

Rewrite the expression

- 27 r^{6} + 5 r^{2} = 0

Solution

More Steps

Evaluate

- 27 r^{6} + 5 r^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

- 27 (x^{2} + y^{2})^{3} + 5 r^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

- 27 (x^{2} + y^{2})^{3} + 5 (x^{2} + y^{2})

Simplify the expression

- 27 x^{6} - 81 x^{4} y^{2} - 81 x^{2} y^{4} - 27 y^{6} + 5 x^{2} + 5 y^{2}

- 27 x^{6} - 81 x^{4} y^{2} - 81 x^{2} y^{4} - 27 y^{6} + 5 x^{2} + 5 y^{2} = 0

Show Solution

Solve the equation

Rewrite the equation

Graph