Solve 4r^2 - 28r^32 = 0

Evaluate

4 r^{2} - 28 r^{3} \times 2 = 0

Evaluate

4 r^{2} - 56 r^{3} = 0

Use substitution

More Steps

4 x^{2} + 4 y^{2} - 56 r^{3} = 0

Simplify the expression

- 56 r^{3} = - 4 x^{2} - 4 y^{2}

Evaluate

- 56 r^{2} \times r = - 4 x^{2} - 4 y^{2}

Evaluate

- 56 (x^{2} + y^{2}) r = - 4 x^{2} - 4 y^{2}

Square both sides of the equation

(- 56 (x^{2} + y^{2}) r)^{2} = (- 4 x^{2} - 4 y^{2})^{2}

Evaluate

(- 56 (x^{2} + y^{2}))^{2} r^{2} = (- 4 x^{2} - 4 y^{2})^{2}

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

(- 56 (x^{2} + y^{2}))^{2} (x^{2} + y^{2}) = (- 4 x^{2} - 4 y^{2})^{2}

Use substitution

(3136 x^{4} + 6272 x^{2} y^{2} + 3136 y^{4}) (x^{2} + y^{2}) = (- 4 x^{2} - 4 y^{2})^{2}

Evaluate the power

(3136 x^{4} + 6272 x^{2} y^{2} + 3136 y^{4}) (x^{2} + y^{2}) = (4 x^{2} + 4 y^{2})^{2}

Divide both sides of the equation by 16

(196 x^{4} + 392 x^{2} y^{2} + 196 y^{4}) (x^{2} + y^{2}) = (x^{2} + y^{2})^{2}

Solution

196 x^{6} + 588 x^{4} y^{2} + 588 x^{2} y^{4} + 196 y^{6} = x^{4} + 2 x^{2} y^{2} + y^{4}

Solve the equation