Solve (x^2)^2=9(x^2-4x^4)

Question

Solve the equation

x_{1} = - \frac{3 37}{37}, x_{2} = 0, x_{3} = \frac{3 37}{37}

Alternative Form

x_{1} \approx - 0.493197, x_{2} = 0, x_{3} \approx 0.493197

Evaluate

(x^{2})^{2} = 9 (x^{2} - 4 x^{4})

Simplify

More Steps

x^{4} = 9 (x^{2} - 4 x^{4})

Expand the expression

More Steps

x^{4} = 9 x^{2} - 36 x^{4}

Move the expression to the left side

x^{4} - (9 x^{2} - 36 x^{4}) = 0

Subtract the terms

More Steps

37 x^{4} - 9 x^{2} = 0

Factor the expression

x^{2} (37 x^{2} - 9) = 0

Separate the equation into 2 possible cases

x^{2} = 0 37 x^{2} - 9 = 0

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

x = 0 37 x^{2} - 9 = 0

Solve the equation

More Steps

x = 0 x = \frac{3 37}{37} x = - \frac{3 37}{37}

Solution

x_{1} = - \frac{3 37}{37}, x_{2} = 0, x_{3} = \frac{3 37}{37}

Alternative Form

x_{1} \approx - 0.493197, x_{2} = 0, x_{3} \approx 0.493197

Show Solution