Solve 5r^39r^2 = 2r^2

Question

Solve the equation

r_{1} = 0, r_{2} = \frac{3 150}{15}

Alternative Form

r_{1} = 0, r_{2} \approx 0.35422

Evaluate

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

Multiply

More Steps

Evaluate

5 r^{3} \times 9 r^{2}

Multiply the terms

45 r^{3} \times r^{2}

Multiply the terms with the same base by adding their exponents

45 r^{3 + 2}

Add the numbers

45 r^{5}

45 r^{5} = 2 r^{2}

Add or subtract both sides

45 r^{5} - 2 r^{2} = 0

Factor the expression

r^{2} (45 r^{3} - 2) = 0

Separate the equation into 2 possible cases

r^{2} = 0 45 r^{3} - 2 = 0

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

r = 0 45 r^{3} - 2 = 0

Solve the equation

More Steps

Evaluate

45 r^{3} - 2 = 0

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

45 r^{3} = 0 + 2

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

45 r^{3} = 2

Divide both sides

\frac{45 r ^{3}}{45} = \frac{2}{45}

Divide the numbers

r^{3} = \frac{2}{45}

Take the 3 -th root on both sides of the equation

3 r^{3} = 3 \frac{2}{45}

Calculate

r = 3 \frac{2}{45}

Simplify the root

More Steps

Evaluate

3 \frac{2}{45}

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

\frac{3 2}{3 45}

Multiply by the Conjugate

\frac{3 2 \times 3 4 5 ^{2}}{3 45 \times 3 4 5 ^{2}}

Simplify

\frac{3 2 \times 3 3 75}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

\frac{3 3 150}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

\frac{3 3 150}{45}

Cancel out the common factor 3

\frac{3 150}{15}

r = \frac{3 150}{15}

r = 0 r = \frac{3 150}{15}

Solution

r_{1} = 0, r_{2} = \frac{3 150}{15}

Alternative Form

r_{1} = 0, r_{2} \approx 0.35422

Show Solution

Rewrite the equation

2025 x^{10} + 10125 x^{8} y^{2} + 20250 x^{6} y^{4} + 20250 x^{4} y^{6} + 10125 x^{2} y^{8} + 2025 y^{10} = 4 x^{4} + 8 x^{2} y^{2} + 4 y^{4}

Evaluate

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

Evaluate

More Steps

Evaluate

5 r^{3} \times 9 r^{2}

Multiply the terms

45 r^{3} \times r^{2}

Multiply the terms with the same base by adding their exponents

45 r^{3 + 2}

Add the numbers

45 r^{5}

45 r^{5} = 2 r^{2}

Rewrite the expression

45 r^{5} - 2 r^{2} = 0

Use substitution

More Steps

Evaluate

45 r^{5} - 2 r^{2}

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

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

Simplify the expression

45 r^{5} - 2 x^{2} - 2 y^{2}

45 r^{5} - 2 x^{2} - 2 y^{2} = 0

Simplify the expression

45 r^{5} = 2 x^{2} + 2 y^{2}

Evaluate

45 r^{4} \times r = 2 x^{2} + 2 y^{2}

Evaluate

45 (x^{2} + y^{2})^{2} r = 2 x^{2} + 2 y^{2}

Square both sides of the equation

(45 (x^{2} + y^{2})^{2} r)^{2} = (2 x^{2} + 2 y^{2})^{2}

Evaluate

(45 (x^{2} + y^{2})^{2})^{2} r^{2} = (2 x^{2} + 2 y^{2})^{2}

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

(45 (x^{2} + y^{2})^{2})^{2} (x^{2} + y^{2}) = (2 x^{2} + 2 y^{2})^{2}

Use substitution

2025 (x^{2} + y^{2})^{5} = (2 x^{2} + 2 y^{2})^{2}

Solution

2025 x^{10} + 10125 x^{8} y^{2} + 20250 x^{6} y^{4} + 20250 x^{4} y^{6} + 10125 x^{2} y^{8} + 2025 y^{10} = 4 x^{4} + 8 x^{2} y^{2} + 4 y^{4}

Show Solution

Solve the equation

Rewrite the equation

Graph