Solve 10/7 - 1/7 r=- 2/7 r^25/7

Question

Solve the equation(The real numbers system)

r \in / R

Alternative Form

No real solution

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Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

r_{1} = \frac{7}{20} - \frac{2751}{20} i, r_{2} = \frac{7}{20} + \frac{2751}{20} i

Alternative Form

r_{1} \approx 0.35 - 2.622499 i, r_{2} \approx 0.35 + 2.622499 i

Show Solution

- 1351 x^{2} - 1351 y^{2} = 100 x^{4} + 100 y^{4} + 4900 + 200 x^{2} y^{2}

Evaluate

\frac{10}{7} - \frac{1}{7} r = - \frac{2}{7} r^{2} \times \frac{5}{7}

Evaluate

More Steps

\frac{10}{7} - \frac{1}{7} r = - \frac{10}{49} r^{2}

Multiply both sides of the equation by LCD

(\frac{10}{7} - \frac{1}{7} r) \times 49 = - \frac{10}{49} r^{2} \times 49

Simplify the equation

More Steps

70 - 7 r = - \frac{10}{49} r^{2} \times 49

Simplify the equation

70 - 7 r = - 10 r^{2}

Rewrite the expression

- 7 r + 10 r^{2} = - 70

Use substitution

More Steps

- 7 r + 10 x^{2} + 10 y^{2} = - 70

Simplify the expression

- 7 r = - 10 x^{2} - 10 y^{2} - 70

Square both sides of the equation

(- 7 r)^{2} = (- 10 x^{2} - 10 y^{2} - 70)^{2}

Evaluate

49 r^{2} = (- 10 x^{2} - 10 y^{2} - 70)^{2}

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

49 (x^{2} + y^{2}) = (- 10 x^{2} - 10 y^{2} - 70)^{2}

Evaluate the power

49 (x^{2} + y^{2}) = (10 x^{2} + 10 y^{2} + 70)^{2}

Calculate

49 x^{2} + 49 y^{2} = 100 x^{4} + 100 y^{4} + 4900 + 200 x^{2} y^{2} + 1400 x^{2} + 1400 y^{2}

Move the expression to the left side

49 x^{2} + 49 y^{2} - (1400 x^{2} + 1400 y^{2}) = 100 x^{4} + 100 y^{4} + 4900 + 200 x^{2} y^{2}

Calculate

More Steps

- 1351 x^{2} + 49 y^{2} = 100 x^{4} + 100 y^{4} + 4900 + 200 x^{2} y^{2} + 1400 y^{2}

Solution

More Steps

- 1351 x^{2} - 1351 y^{2} = 100 x^{4} + 100 y^{4} + 4900 + 200 x^{2} y^{2}

Show Solution