Solve 5x^2-11x^4=0

Question

Solve the equation

x_{1} = - \frac{55}{11}, x_{2} = 0, x_{3} = \frac{55}{11}

Alternative Form

x_{1} \approx - 0.6742, x_{2} = 0, x_{3} \approx 0.6742

Evaluate

5 x^{2} - 11 x^{4} = 0

Factor the expression

x^{2} (5 - 11 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 - 11 x^{2} = 0

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

x = 0 5 - 11 x^{2} = 0

Solve the equation

More Steps

Evaluate

5 - 11 x^{2} = 0

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

- 11 x^{2} = 0 - 5

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

- 11 x^{2} = - 5

Change the signs on both sides of the equation

11 x^{2} = 5

Divide both sides

\frac{11 x ^{2}}{11} = \frac{5}{11}

Divide the numbers

x^{2} = \frac{5}{11}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{5}{11}

Simplify the expression

More Steps

Evaluate

\frac{5}{11}

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

\frac{5}{11}

Multiply by the Conjugate

\frac{5 \times 11}{11 \times 11}

Multiply the numbers

\frac{55}{11 \times 11}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{55}{11}

x = \pm \frac{55}{11}

Separate the equation into 2 possible cases

x = \frac{55}{11} x = - \frac{55}{11}

x = 0 x = \frac{55}{11} x = - \frac{55}{11}

Solution

x_{1} = - \frac{55}{11}, x_{2} = 0, x_{3} = \frac{55}{11}

Alternative Form

x_{1} \approx - 0.6742, x_{2} = 0, x_{3} \approx 0.6742

Show Solution