Solve r^222r - 13 = 0

Question

Solve the equation

r = \frac{3 6292}{22}

Alternative Form

r \approx 0.839151

Evaluate

r^{2} \times 22 r - 13 = 0

Multiply

More Steps

Evaluate

r^{2} \times 22 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 22

Add the numbers

r^{3} \times 22

Use the commutative property to reorder the terms

22 r^{3}

22 r^{3} - 13 = 0

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

22 r^{3} = 0 + 13

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

22 r^{3} = 13

Divide both sides

\frac{22 r ^{3}}{22} = \frac{13}{22}

Divide the numbers

r^{3} = \frac{13}{22}

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

3 r^{3} = 3 \frac{13}{22}

Calculate

r = 3 \frac{13}{22}

Solution

More Steps

Evaluate

3 \frac{13}{22}

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

\frac{3 13}{3 22}

Multiply by the Conjugate

\frac{3 13 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{3 13 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3484

The product of roots with the same index is equal to the root of the product

3 13 \times 484

Calculate the product

36292

\frac{3 6292}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

322 \times 3 2 2^{2}

The product of roots with the same index is equal to the root of the product

3 22 \times 2 2^{2}

Calculate the product

3 2 2^{3}

Reduce the index of the radical and exponent with 3

22

\frac{3 6292}{22}

r = \frac{3 6292}{22}

Alternative Form

r \approx 0.839151

Show Solution

Rewrite the equation

484 x^{6} + 1452 x^{4} y^{2} + 1452 x^{2} y^{4} + 484 y^{6} = 169

Evaluate

r^{2} \times 22 r - 13 = 0

Evaluate

More Steps

Evaluate

r^{2} \times 22 r - 13

Multiply

More Steps

Evaluate

r^{2} \times 22 r

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 22

Add the numbers

r^{3} \times 22

Use the commutative property to reorder the terms

22 r^{3}

22 r^{3} - 13

22 r^{3} - 13 = 0

Rewrite the expression

22 r^{3} = 13

Evaluate

22 r^{2} \times r = 13

Evaluate

22 (x^{2} + y^{2}) r = 13

Square both sides of the equation

(22 (x^{2} + y^{2}) r)^{2} = 1 3^{2}

Evaluate

(22 (x^{2} + y^{2}))^{2} r^{2} = 1 3^{2}

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

(22 (x^{2} + y^{2}))^{2} (x^{2} + y^{2}) = 1 3^{2}

Use substitution

(484 x^{4} + 968 x^{2} y^{2} + 484 y^{4}) (x^{2} + y^{2}) = 1 3^{2}

Evaluate the power

(484 x^{4} + 968 x^{2} y^{2} + 484 y^{4}) (x^{2} + y^{2}) = 169

Solution

484 x^{6} + 1452 x^{4} y^{2} + 1452 x^{2} y^{4} + 484 y^{6} = 169

Show Solution

Solve the equation

Rewrite the equation

Graph